THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


EAST  ABUTMENT  OF  BLACKWELL'S   ISLAND  BRIDGE,  NEW  YORK 

Copyright,   1907,  by   Underwood   &   Underwood,   New   York. 


JOHfl  S.  PRELL  ' 

Civil  &  Mechanical  Engineer. 

SAN  FRANCISCO,  CAL. 

Cyclopedia 

tf 

Civil   Engineering 


A  General  Reference  Work 

ON   SURVEYING,  RAILROAD   ENGINEERING,  STRUCTURAL   ENGINEERING,   ROOFS 

AND  BRIDGES,    MASONRY   AND   REINFORCED   CONCRETE,    HIGHWAY 

CONSTRUCTION,    HYDRAULIC   ENGINEERING,    IRRIGATION. 

RIVER  AND   HARBOR   IMPROVEMENT,    MUNICIPAL 

ENGINEERING,    COST  ANALYSIS,    ETC. 


Editor-in-  Chief 
FREDERICK  E.  TURNEAURE,  C.  E.,  Dr.  Eng. 

DEAN,    COLLEGE   OF   ENGINEERING,    UNIVERSITY   OF  WISCONSIN 


Assisted  by  a  Corps  of 

CIVIL  AND   CONSULTING  ENGINEERS  AND  TECHNICAL   EXPERTS  OF  THE 
HIGHEST  PROFESSIONAL  STANDING 


Illustrated  with  over  Three  Thousand  Engravings 


EIGHT    VOLUMES 


CHICAGO 
AMERICAN   TECHNICAL   SOCIETY 


COPYRIGHT,   1908 
BY 

AMERICAN  SCHOOL  OF  CORRESPONDENCE 


COPYRIGHT,   1908 
BY 

AMERICAN  TECHNICAL  SOCIETY 


Entered  at  Stationers'  Hall,  London 
All  Rights  Reserved, 


TA 


Editor-in-Chief 
FREDERICK  E.  TURNEAURE,  C.  E.,  Dr.  Eng. 

Dean,  ColJege  of  Engineering,  University  of  Wisconsin 


Authors  and  Collaborators 

WALTER  LORING  WEBB,  C.  E. 

Consulting  Civil  Engineer 

American  Society  of  Civil  Engineers 

Author  of  "Railroad  Construction,  '  "Economics  of  Railroad  Construction,"  etc. 


FRANK  O.  DUFOUR,  C.  E. 

Assistant  Professor  of  Structural  Engineering,  University  of  Illinois 
American  Society  of  Civil  Engineers 
American  Society  for  Testing  Materials 


HALBERT  P.  GILLETTE,  C.  E. 

Consulting  Engineer 
American  Society  of  Civil  Engineers 
Managing  Editor  "Engineering-Contracting" 

Author  of  "Handbook  of  Cost  Data  for  Contractors  and  Engineers,"  "Earthwork 
and  its  Cost,"  "Rock  Excavation—  Methods  and  Cost" 


ADOLPH  BLACK,  C.  E. 

Adjunct  Professor  of  Civil  Engineering,  Columbia  University,  N.  Y. 


EDWARD  R.  MAURER,  B.  C.  E. 

Professor  of  Mechanics,  University  of  Wisconsin 

Joint  Author  of  "Principles  of  Reinforced  Concrete  Construction 


W.  HERBERT  GIBSON,  B.  S.,  C.  E. 

Civil  Engineer 

Designer  of  Reinforced  Concrete 


AUSTIN  T.  BYRNE 

Civil  Engineer 

Author  of  "Highway  Construction,"  "Materials  and  Workmanship 


713592 


Authors  and  Collaborators— Continued 


FREDERICK  E.  TURNEAURE,  C.  E.,  Dr.  Eng. 

Dean  of  the  College  of  Engineering,  and  Professor  of  Engineering,  University  of 

Wisconsin 

American  Society  of  Civil  Engineers 
Joint  Author  of  "Principles  of  Reinforced  Concrete  Construction,"  "Public  Water 

Supplies,"  etc. 


THOMAS  E.  DIAL,  B.  S. 

Instructor  in  Civil  Engineering,  American  School  of  Correspondence 

Formerly  with  Engineering  Department,  Atchison,  Topeka  &  Santa  Fe  Railroad 


ALFRED  E.  PHILLIPS,  C.  E.,  Ph.  D. 

Head  of  Department  of  Civil  Engineering,  Armour  Institute  of  Technology 
^ 

DARWIN  S.  HATCH,  B.  S. 

Instructor  in  Mechanical  Engineering,  American  School  of  Correspondence 


CHARLES  E.  MORRISON,  C.  E.,  A.  M. 

Instructor  in  Civil  Engineering,  Columbia  University,  N.  Y. 
Author  of  "Highway  Engineering." 


ERVIN  KENISON,  S.  B. 

Instructor  in  Mechanical  Drawing,  Massachusetts  Institute  of  Technology 
**• 

EDWARD  B.  WAITE 

Head  of  Instruction  Department,  American  School  of  Correspondence 
American  Society  of  Mechanical  Engineers 
Western  Society  of  Engineers 


EDWARD  A.  TUCKER,  S.  B. 

A  rchitectural  Engineer 

American  Society  of  Civil  Engineers 


ERNEST  L.  WALLACE,  S.  B. 

Instructor  in  Electrical  Engineering,  American  School  of  Correspondence 
American  Institute  of  Electrical  Engineers 


A.  MARSTON,  C.  E. 

Dean  of  Division  of  Engineering  and  Prof  essor  of  Civil  Engineering,  Iowa  State 

College 

American  Society  of  Civil  Engineers 
Western  Society  of  Civil  Engineers 


Authors  and  Collaborators— Continued 


CHARLES  B.  BALL 

Civil  and  Sanitary  Engineer 

Chief  Sanitary  Inspector.  City  of  Chicago 

American  Society  of  Civil  Engineers 


ALFRED  E.  ZAPF,  S.  B. 

Secretary,  American  School  of  Correspondence 

SIDNEY  T.  STRICKLAND,  S.  B. 

Massachusetts  Institute  of  Technology 
Ecole  des  Beaux  Arts,  Paris 

RICHARD  T.  DANA 

Consulting  Engineer 

American  Society  of  Civil  Engineers 

Chief  Engineer,  Construction  Service  Co. 

^« 

ALFRED  S.  JOHNSON,  A.  M.,  Ph.  D. 

Textbook  Department,  American  School  of  Correspondence 
Formerly  Instructor,  Cornell  University 
Royal  Astronomical  Society  of  Canada 


WILLIAM  BEALL  GRAY 

Sanitary  Engineer 

National  Association  of  Master  Plumbers 

United  Association  of  Journeyman  Plumbers 


R.  T.  MILLER,  Jr.,  A.  M.,  LL.  B. 

President  American  School  of  Correspondence 


GEORGE  R.  METCALFE,  M.  E. 

Head  of  Technical  Publication  Department,  Westinghouse  Electric  &  Manufac- 

turing Co. 

Formerly  Technical  Editor,  "Street-  Rail  way  Review" 
Formerly  Editor  "The  Technical  World  Magazine" 


MAURICE  LE  BOSQUET,  S.  B. 

Massachusetts  Institute  of  Technology 

British  Society  of  Chemical  Industry,  American  Chemical  Society,  etc. 


HARRIS  C.  TROW,  S.  B.,  Managing  Editor 

Editor  of  Textbook  Department,  American  School  of  Correspondence 
American  Institute  of  Electrical  Engineers 


Authorities    Consulted 


THE  editors  have  freely  consulted  the  standard  technical  literature  of 
America  and  Europe  in  the  preparation  of  these  volumes.    They  desire 
to  express  their  indebtedness,  particularly,  to  the  following  eminent 
authorities,  whose  well-known  treatises  should  be  in  the  library  of  everyone 
interested  in  Civil  Engineering. 

Grateful  acknowledgment  is  here  made  also  for  the  invaluable  co-opera- 
tion of  the  foremost  Civil,  Structural,  Railroad,  Hydraulic,  and  Sanitary 
Engineers  in  making  these  volumes  thoroughly  representative  of  the  very 
best  and  latest  practice  in  every  branch  of  the  broad  field  of  Civil  Engineer- 
ing; also  for  the  valuable  drawings  and  data,  illustrations,  suggestions, 
criticisms,  and  other  courtesies. 


WILLIAM  G.  RAYMOND,  C.  E. 

Dean  of  the  School  of  Applied  Science  and  Professor  of  Civil  Engineering  in  the  State 

University  of  Iowa;  American  Society  of  Civil  Engineers. 

Author  of  "A  Textbook  of  Plane  Surveying,"  "The  Elements  of  Railroad  Engineering." 
V 

JOSEPH  P.  FRIZELL 

Hydraulic  Engineer  and  Water-Power  Expert;  American  Society  of  Civil  Engineers. 
Author  of  "  Water  Power,  the  Development  and  Application  of  the  Energy  of  Flowing 
Water."  ^ 

FREDERICK  E.  TURNEAURE,  C.  E.,  Dr.  Eng. 

Dean  of  the  College  of  Engineering  and  Professor  of  Engineering,  University  of  Wisconsin. 
Joint  Author  of  "Public  Water  Supplies,"  "Theory  and  Practice  of  Modern  Framed 
Structures,"  "  Principles  of  Reinforced  Concrete  Construction." 
^ 

H.  N.  OGDEN,  C.  E. 

Assistant  Professor  of  Civil  Engineering,  Cornell  University. 
Author  of  "Sewer  Design." 

^* 

DANIEL  CARHART,  C.  E. 

Professor  of  Civil  Engineering  in  the  Western  University  of  Pennsylvania. 
Author  of  "A  Treatise  on  Plane  Surveying." 
** 

HALBERT  P.  GILLETTE 

Editor  of  Engineering -Contracting;  American  Society  of  Civil  Engineers;  Late  Chief 

Engineer,  Washington  State  Railroad  Commission. 
Author  of  "  Handbook  of  Cost  Data  for  Contractors  and  Engineers." 


CHARLES  E.  GREENE,  A.  M.,  C.  E. 

Late  Professor  of  Civil  Engineering,  University  of  Michigan. 

Author  of  "Trusses  and  Arches,  Graphic  Method,"  "Structural  Mechanics.' 


Authorities  Consulted— Continued 


A.  PRESCOTT  FOLWELL 

Editor  of  Municipal  Journal  and  Engineer;  Formerly  Professor  of  Municipal  Engineer- 
ing, Lafayette  College. 
Author  of  "  Water  Supply  Engineering, "  "Sewerage." 


LEVESON  FRANCIS  VERNON-HARCOURT,  M.  A. 

Emeritus  Professor  of  Civil  Engineering  and  Surveying,  University  College,  London; 
Institution  of  Civil  Engineers. 

Author  of  "Rivers  and  Canals,"  "Harbors  and  Docks,"  "Achievements  in  Engineer- 
ing," "  Civil  Engineering  as  Applied  in  Construction." 


PAUL  C.  NUGENT,  A.  M.,  C.  E. 

Professor  of  Civil  Engineering,  Syracuse  University. 
Author  of  "  Plane  Surveying." 

*>• 

FRANK  W.  SKINNER 

Consulting  Engineer;  Associate  Editor  of  The  Engineering  Record;  Non-Resident  Lec- 
turer on  Field  Engineering  in  Cornell  University. 
Author  of  "  Types  and  Details  of  Bridge  Construction." 


HANBURY  BROWN,  K.  C.  M.  G. 

Member  of  the  Institution  of  Civil  Engineers. 
Author  of  "  Irrigation,  Its  Principles  and  Practice." 


SANFORD  E.  THOMPSON,  S.  B.,  C.  E. 

American  Society  of  Civil  Engineers. 

Joint  Author  of  "A  Treatise  on  Concrete,  Plain  and  Reinforced.' 


JOSEPH  KENDALL  FREITAG,  B.  S.,  C.  E. 

American  Society  of  Civil  Engineers. 

Author  of  "Architectural  Engineering,"  "  Fireproofing  of  Steel  Buildings." 

*>• 

AUSTIN  T.  BYRNE,  C.  E. 

Civil  Engineer. 

Author  of  "Highway  Construction,"  "Inspection  of  Materials  and  Workmanship  Em- 
ployed in  Construction." 

^» 

JOHN  F.  HAYFORD,  C.  E. 

Inspector  of  Geodetic  Work  and  Chief  of  Computing  Division,  Coast  and  Geodetic  Survey; 

American  Society  of  Civil  Engineers. 
Author  of  "A  Textbook  of  Geodetic  Astronomy." 


WALTER  LORING  WEBB,  C.  E. 

Consulting  Civil  Engineer;  American  Society  of  Civil  Engineers. 

Author  of  "Railroad  Construction   in  Theory  and  Practice,"  "Economics  of  Railroad 
Construction,"  etc. 


Authorities  Consulted— Continued 


EDWARD  R.  MAURER,  B.  C.  E. 

Professor  of  Mechanics,  University  of  Wisconsin. 
Joint  Author  of  "  Principles  of  Reinforced  Concrete  Construction." 
*r* 

HERBERT  M.  WILSON,  C.  E. 

Geographer  and  Former  Irrigation  Engineer.  United  States  Geological  Survey;  American 

Society  of  Civil  Engineers. 
Author  of  "  Topographic  Surveying."  "  Irrigation  Engineering,"  etc. 


MANSFIELD  MERRIMAN,  C.  E.,  Ph.  D. 

Professor  of  Civil  Engineering,  Lehigh  University. 

Author  of  "  The  Elements  of  Precise  Surveying  and  Geodesy,"  "A  Treatise  on  Hydraul- 
ics," "Mechanics  of  Materials,"  "Retaining  Walls  and  Masonry  Dams,"  "Introduction 
to  Geodetic  Surveying,"  "A  Textbook  on  Roofs  and  Bridges,"  "A  Handbook  for 
Surveyors,''  etc. 

^* 

DAVID  M.  STAUFFER 

American  Society  of  Civil  Engineers;   Institution  of  Civil  Engineers;   Vice-  President, 

Engineering  News  Publishing  Co. 
Author  of  '  Modern  Tunnel  Practice." 

**• 

CHARLES  L.  CRANDALL 

Professor  of  Railroad  Engineering  and  Geodesy  in  Cornell  University. 
Author  of  "A  Textbook  on  Geodesy  and  Least  Squares." 


N.  CLIFFORD  RICKER,  M.  Arch. 

Professor  of  Architecture,  University  of  Illinois;  Fellow  of  the  American  Institute  of 

Architects  and  of  the  Western  Association  of  Architects. 

Author  of  "  Elementary  Graphic  Statics  and  the  Construction  of  Trussed  Roofs." 
^« 

JOHN  C.  TRAUTWINE 

Civil  Engineer. 

Author  of  "The  Civil  Engineer's  Pocketbook." 
^ 

HENRY  T.  BOVEY 

Professor  of  Civil  Engineering  and  Applied  Mechanics,  McGill  University,  Montreal. 
Author  of  "A  Treatise  on  Hydraulics." 

^• 

WILLIAM  H.  BIRKMIRE,  C.  E. 

Author  of  "Planning  and  Construction  of  High  Office  Buildings,"  "Architectural  Iron 
and  Steel,  and  Its  Application  in  the  Construction  of  Buildings,"  "  Compound  Riv- 
eted Girders,"  'Skeleton  Structures,'   etc. 
^- 

IRA  0.  BAKER,  C.  E. 

Professor  of  Civil  Engineering,  University  of  Illinois. 

Author  of  "A  Treatise  on  Masonry  Construction,"  "  Engineers'  Surveying  Instruments, 
Their  Construction,  Adjustment,  and  Use,"  "Roads  and  Pavements." 


Authorities  Consulted— Continued 


JOHN  CLAYTON  TRACY,  C.  E. 

Assistant  Professor  of  Structural  Engineering,  Sheffield  Scientific  School,  Yale  University. 
Author  of  "  Plane  Surveying:  A  Textbook  and  Pocket  Manual." 


FREDERICK  W.  TAYLOR,  M.  E. 

Joint  Author  of  "A  Treatise  on  Concrete,  Plain  and  Reinforced." 
^« 

JAMES  J.  LAWLER 

Author  of  "  Modern  Plumbing,  Steam  and  Hot-  Water  Heating." 


FRANK  E.  KIDDER,  C.  E.,  Ph.  D. 

Consulting  Architect  and  Structural  Engineer;    Fellow  of  the  American  Institute  of 
Architects. 

Author  of  "Architect's  and  Builder's  Pocketbook,"  "  Building  Construction  and  Super- 
intendence, Part  I,  Masons'  Work;  Part  II,  Carpenters'  Work;  Part  III,  Trussed  Roofs 
and  Roof  Trusses,"  "  Strength  of  Beams,  Floors,  and  Roofs." 
^« 

WILLIAM  H.  BURR,  C.  E. 

Professor  of  Civil  Engineering,  Columbia  University;   Consulting  Engineer;   American 

Society  of  Civil  Engineers;  Institution  of  Civil  Engineers. 
Author  of  "  Elasticity  and  Resistance  of  the  Materials  of  Engineering;"  Joint  Author  of 

"  The  Design  and  Construction  of  Metallic  Bridges." 


WILLIAM  M.  GILLESPIE,  LL.  D. 

Formerly  Professor  of  Civil  Engineering  in  Union  University. 
Author  of  "  Land  Surveying  and  Direct  Leveling,"  "  Higher  Surveying." 
*r> 

GEORGE  W.  TILLSON,  C.  E. 

President  of  the  Brooklyn  Engineers'  Club;  American  Society  of  Civil  Engineers;  Ameri- 
can Society  of  Municipal  Improvements;  Principal  Assistant  Engineer,  Department 
of  Highways,  Brooklyn. 

Author  of  "  Street  Pavements  and  Street  Paving  Material." 
*** 

G.  E.  FOWLER 

Civil  Engineer;  President,  The  Pacific  Northwestern  Society  of  Engineers;    American 

Society  of  Civil  Engineers. 
Author  of  "  Ordinary  Foundations." 

^ 

WILLIAM  M.  CAMP 

Editor  of  The  Railway  and  Engineering  Review;  American  Society  of  Civil  Engineers. 
Author  of  "  Notes  on  Track  Construction  and  Maintenance." 


W.  M.  PATTON 


Late  Professor  of  Engineering  at  the  Virginia  Military  Institute. 
Author  of  "A  Treatise  on  Civil  Ensrineerinrr." 


Foreword 


HE  marvelous  developments  of  the  present  day  in  the  field 
of  Civil  Engineering,  as  seen  in  the  extension  of  railroad 
lines,  the  improvement  of  highways  and  waterways,  the 
increasing  application  of  steel  and  reinforced  concrete 
to  construction  work,  the  development  of  water  power 
and  irrigation  projects,  etc.,  have  created  a  distinct  necessity 
for  an  authoritative  work  of  general  reference  embodying  the 
results  and  methods  of  the  latest  engineering  achievement. 
The  Cyclopedia  of  Civil  Engineering  is  designed  to  fill  this 
acknowledged  need. 

C,  The  aim  of  the  publishers  has  been  to  create  a  work  which, 
while  adequate  to  meet  all  demands  of  the  technically  trained 
expert,  will  appeal  equally  to  the  self-taught  practical  man, 
who,  as  a  result  of  the  unavoidable  conditions  of  his  environ- 
ment, may  be  denied  the  advantages  of  training  at  a  resident 
technical  school.  The  Cyclopedia  covers  not  only  the  funda- 
mentals that  underlie  all  civil  engineering,  but  their  application 
to  all  types  of  engineering  problems;  and,  by  placing  the  reader 
in  direct  contact  with  the  experience  of  teachers  fresh  from 
practical  work,  furnishes  him  that  adjustment  to  advanced 
modern  needs  and  conditions  which  is  a  necessity  even  to  the 
technical  graduate. 


C.  The  Cyclopedia  of  Civil  Engineering  is  a  compilation  of 
representative  Instruction  Books  of  the  American  School  of  Cor- 
respondence, and  is  based  upon  the  method  which  this  school 
has  developed  and  effectively  used  for  many  years  in  teaching 
the  principles  and  practice  of  engineering  in  its  different 
branches.  The  success  attained  by  this  institution  as  a  factor 
in  the  machinery  of  modern  technical  education  is  in  itself  the 
best  possible  guarantee  for  the  present  work. 

C,  Therefore,  while  these  volumes  are  a  marked  innovation  in 
technical  literature  —  representing,  as  they  do,  the  best  ideas  and 
methods  of  a  large  number  of  different  authors,  each  an  ac- 
knowledged authority  in  his  work  —  they  are  by  no  means  an 
experiment,  but  are  in  fact  based  on  what  long  experience  has 
demonstrated  to  be  the  best  method  yet  devised  for  the  educa- 
tion of  the  busy  workingman.  They  have  been  prepared  only 
after  the  most  careful  study  of  modern  needs  as  developed 
under  conditions  of  actual  practice  at  engineering  headquarters 
and  in  the  field. 

C.  Grateful  acknowledgment  is  due  the  corps  of  authors  and 
collaborators  —  engineers  of  wide  practical  experience,  and 
teachers  of  well-recognized  ability  —  without  whose  co-opera- 
tion this  work  would  have  been  impossible. 


Table   of  Contents 


VOLUME  VI 
BRIDGE  ENGINEERING  By  Frank  O.  Dufourf       Page  *11 

Bridge  Analysis  —  Early  Bridges  —  Trusses  —  Girders  —  Truss  and  Girder  Bridges 

—  Deck  and  Through  Bridges  —  Truss  Members  —  Lateral  Bracing  —  Portals  — 
Sway  Bracing  —  Knee-Braces  —  Kinds  of  Trusses  —  Chord  and  Web  Character- 
istics —  Weights  of  Bridges  —  Loads  (Dead,  Live,  Wind)  —  Principles  of  Analysis 

—  Resolution  of  Forces  —  Method  of  Moments  —  Stresses   in  Web  and    Chord 
Members  —  Warren  Truss  under  Live  and  Dead  Loads  —  Position  of  Live  Load 
for  Maximum  Moments  —  Counters  —  Maximum  and  Minimum  Stresses  —  Pratt, 
Howe,  Baltimore,  Bowstring,  Parabolic,  and  Other  Trusses  under  Dead  and  Live 
Loads  —  Engine  Loads  —  Position  of  Wheel  Loads  for  Maximum  Shear  and  Mo- 
ments —  Pratt    Truss    under    Engine    Loads  —  Impact    Stresses  —  Snow- Load 
Stresses  —  Wind-Load  Effects  —  Top  and  Bottom  Lateral  Bracing  —  Overturning 

—  Pratt  Truss  under  Wind  Loads  —  Girder  Spans  —  Floor- Beam    Reactions  — 
Plate-Girder  Reactions  —  Bridge  Design  —  Economic  Considerations  —  Types  of 
Bridges  for  Various  Spans  —  Economic   Proportions  of    Members  —  Clearance 
Diagram  —  Weights  and  Loadings  —  Specifications  —  Stress  Sheet  —  Design  of  a 
Plate-Girder  Railway  Span  —  Masonry  Plan  —  Determination  of  Span  —  Ties  and 
Guard -Rails  —  Web  and  Flanges  —  Rivet  Spacing  —  Lateral  Systems  and  Cross- 
Frames  —  Stiffeners  —  Web-Splice  —  Bearings  —  Design  of  a  Through  Pratt  Rail- 
way Span  —  Stringers  —  Floor-  Beams  —  Tension  Members  —  Intermediate  Posts  — 
Lacing  Bars  —  End -Posts  —  Pins  —  Transverse  Bracing  —  Shoes  and  Roller  Nests 

HIGHWAY  CONSTRUCTION   .   By  A.  T.  Byrne  and  A.  E.Phillips        Page  267 

Country  Roads  —  Road  Resistances  to  Traction  —  Axle  Friction  —  Air  Resistance 

—  Tractive  Power  and  Gradients  —  Effects  of  Springs  on  Vehicles  —  Location  of 
Roads  —  Contour  Lines  —  Levels  —  Cross-Levels  —  Bridge  Sites  —  Mountain  Roads 

—  Alignment  —  Zigzags  —  Construction  Profile  —  Width  and  Transverse  Contour 

—  Drainage  Ditches  and  Culverts  —  Earthwork  —  Roads  on  Rocky  Slopes  —  Earth 
and  Sand  Roads  —  Grading  Tools  — •-  Rollers  —  Sprinkling  Carts  —  Road  Coverings 

—  Gravel  Roads  —  Macadam  Roads  — City  Streets  — Catch- Basins  — Pavement 
Foundations  —  Stone- Block    Pavements  —  Properties    of    Stones  —  Cobblestone 
Pavement  —  Belgian  Block  Pavement  —  Brick  Pavement  —  Paving  Brick  —  Con- 
crete Mixers  —  Gravel  Heaters  —  Melting  Furnaces  —  Wood  Pavements  —  Asphalt 
Pavements  —  Mixing    Formulae  —  Footpaths  —  Curbstones  —  Artificial    Stone  — 
Pavement  Selection  —  Safety  —  Life  of  Pavements  —  Cost  —  Relative  Economies 

REVIEW  QUESTIONS Page  399 

INDEX Page  405 


*For  page  numbers,  see  foot  of  pages. 

TFor  professional  standing  of  authors,  see  list  of  Authors  and  Collaborators  at 


BRIDGE  ENGINEERING 

PART  I 


BRIDGE    ANALYSIS 

1.  Introduction.    The  following  treatment  of  the  subject  of 
Bridge  Analysis,  while  not  exhaustive,  is  regarded  as   sufficiently 
elaborate  to  develop  and  instill  the  principal  theoretical  considera- 
tions, to  illustrate  the  most  convenient  and  practical  methods  of 
analyzing  the  common  forms  of  trusses  and  girders,  and  also  to  lay 
a  sufficient  foundation  for  the  analysis  of  such  other  trusses  as  are 
not  specifically  mentioned  or  treated  herein. 

The  necessary  steps  and  operations  required  for  a  proper  analysis 
of  the  several  types  of  bridges  are  fully  demonstrated  by  sketches 
and  computations,  the  numerical  values  being  mechanically  obtained 
by  the  use  of  a  slide  rule,  which  is  a  handy  instrument  for  quickly 
performing  the  operations  of  multiplication  and  division,  and  for 
squaring  and  extracting  the  roots  of  numbers.  The  values  given 
may  differ  from  the  exact  value  by  one  unit  in  the  second  decimal 
place  (seldom  more)  and  are  sufficiently  accurate  for  the  purpose  of 
design.  All  bridge  computers  should  be  proficient  in  the  use  of  the 
slide  rule. 

The  problems  given  in  the  back  of  this  Instruction  Paper, 
exemplifying  the  practical  application  of  the  subject-matter  treated 
in  the  various  articles,  should  be  solved  by  the  student  as  each  article 
is  mastered. 

HISTORY 

2.  Early  Bridges.    Early  bridges  were  not  bridges  according 
to   the  present  conception  of  the   term.     They  were  simple  pile 
trestle  bents  placed  at  frequent  intervals  and  connected  by  wooden 
beams  on  which  the  floor  was  placed.     The  Pans  sublicius,  built  over 
the  Tiber,  at  Rome,  about  650  years  before  Christ  was  born,  was  of 
this  trestle  type.    Also  the  famous  bridge  b'uilt  by  Csesar  across  the 
Rhine  in  55  B.  C.  was  of  the  same  kind  of  construction.     As  civiliza- 
tion progressed,  the  arch  type  was  developed;  and  in  1390  the  great 

Copyright,  190S,  by  American  School  of  Corespondence. 


11 


BRIDGE  ENGINEERING 


bridge  at  Trezzo  over  the  River  Adda  was  built  of  one  span  of  251 
feet,  which  has  never  been  eclipsed  or  equaled. 

3.  Truss  Bridge  Development.  The  first  truss  bridge  is  sup- 
posed to  have  been  originated  by  Palladio,  an  Italian,  who  used  the 
king-post  truss  (Fig.  1)  about  1570.  Its  importance  was  not  recog- 
nized, and  it  became  entirely  for- 
gotten until  it  was  rediscovered  in 
1798  by  Theodore  Burr,  an  Ameri- 
can, who  used  it  in  his  construction. 
About  the  same  time,  Burr  invented 
the  truss  that  bears  his  name, 
which  was  in  reality  a  series  of 
king-post  trusses  (see  Fig.  8).  This 
was  found  to  be  unstable  under  moving  loads,  and  was  therefore 
stiffened  by  the  use  of  an  arch  (Fig.  2),  or  was  built  somewhat  as  an 
arch,  there  being  considerable  rise  at  the  center  of  the  span  (Fig.  3). 
By  1830  the  principle  of  the  double  cross-bracing  in  the  panel  was 
understood;  and  in  quick  succession  came  the  patents  of  Long, 
Howe,  Pratt,  and  Whipple  on  forms  of  trusses  which  bear  their 
respective  names. 

It  remained  for  Squire  Whipple  in  1847  to  place  the  science  of 
bridge   building  on   a   rational  and  exact  mathematical  basis  such 


Fig.  l.    King-Post  Truss. 


Fig.  2.    King-Post  Truss  Bridge  Stiffened  by  Arch. 

as  is  now  used.  Previous  to  this  time,  and  indeed  several  years 
afterwards — for  Whipple's  work  did  not  become  generally  known 
until  a  much  later  date — bridges  were  built,  not  from  previously 
computed  strains,  but  by  "judgment."  All  parts  of  a  bridge  were 
made  of  the  same  size,  and  if  one  started  to  fail  it  was  replaced  by 
a  larger  one;  or  small  models  were  made  and  loaded  proportionally, 
broken  members  being  replaced  by  larger  ones.  There  is  no  doubt 


12 


BRIDGE  ENGINEERING 


that  many  of  the  bridges  built  at  this  period  were  very  weak  as  well 
as  very  strong.  The  failures  are  not  remembered;  but  the  sound 
judgment  of  many  of  our  earlier  bridge  engineers  is  recorded  in  the 
wooden  structures  they  left  behind  them,  some  of  which  have  stood 
the  demands  of  traffic  for  over  a  century.  After  1850,  bridges  were 
built  from  computed  stresses;  wood  was  discarded;  and  the  develop- 
ment became  rapid,  until  about  1870,  when  the  introduction  of  sub- 
diagonal  systems  brought  the  truss  system  to  practically  what  it  is 
to-day. 

DEFINITIONS  AND  DESCRIPTIONS 

4.    Trusses.    A  truss  is  a  series  of  members  taking  stress  in 
the  direction  of  their  length,  placed  together  so  as  to  form  a  triangle 


Fig.  3.    Burr  Tru^s  Bridge,  Arched. 

or  system  of  triangles,  which,  when  placed  upon  supports  a  certain 
distance  apart,  will,  in  addition  to  their  own  weight,  sustain  certain 
loads  applied  at  the  points  where  the  members  intersect.  These 
points  are  called  panel  points. 

5.  Bridge  Trusses.    A  bridge  truss  is  one  in  wrhich  the  members 
that  carry  the  superimposed  loads  are  in  the  same  plane.     Usually 
this  plane  is  vertical. 

6.  Truss  Bridges.    A  truss  bridge  is  a  structure  consisting  of 
two  or  more — usually  two — bridge  trusses  connected  by  a  system 
of  beams  called  the  floor  system,  which  transfer  to  panel  points  the 
load  for  which  the  trusses  are  designed. 

7.  Girders.     These  are  beams  consisting  of  a  wide,  thin  plate, 
called  a    web  plate,  with  shapes,  usually   angles  and  narrow,  thin 
plates  called  flanges,  at  the  top  and  bottom  edges.     All  are  firmly 
riveted  together.     (See  Part  IV,  "Steel  Construction.") 

8.  Girder  Bridges.    These  consist  of  usually  two,  sometimes 


13 


BRIDGE  ENGINEERING 


three,  girders  connected  as  in  the  case  of  truss  bridges  by  a  system 
of  beams. 

9.  Deck  Bridges.  In  cases  where  the  floor  system  connects 
the  trusses  at  their  tops,  the  bridge  is  called  a  deck  bridge,  since  the 
traffic  moves  on  a  deck,  as  it  were  (see  Fig.  4). 


Fig.  4.    Deck  Bridge. 


Fig.  5.    Through  Bridge. 

10.  Through  Bridges.     In  cases  where  the  floor  system  con- 
nects the  bottoms  of  the  trusses,  the  bridge  is  called  a  through  bridge, 
as  the  traffic  moves  through  the  space  between  the  trusses  (see  Fig.  5). 

11.  Members  of  a  Truss.    Each  truss  consists  of  a  top  and 
bottom  chord,  end-posts,  and  web  members.    The  web  members  are 
further  divided  into  hip  verticals,  intermediate  posts,  and  diagonals. 
Fig.   6  shows   these  various  classes,   A-A   being   top  chord,  B-B 


Fig.  6.    Showing  the  Members  of  a  Truss. 


bottom  chord,  A-B  end-posts,  vertical   members   C-b  intermediate 
posts,  A-a  hip  verticals,  and  A-b  and  C-b  diagonals. 

12.  Pony=Truss  Bridges.  When  the  height  of  the  trusses  of 
a  through  bridge  is  less  than  the  height  of  the  loads  that  go  over 
them,  they  are  called  pony  trusses,  and  the  bridge  a  pony-truss  bridge. 


14 


BRIDGE  ENGINEERING 


13.  Lateral  Bracing.  In  all  deck  bridges,  and  in  all  through 
bridges  except  pony-truss  bridges,  the  chords  which  are  not  con- 
nected by  the  floor  system  are  connected  by  a  horizontal  truss  system 
called  the  lateral  bracing.  In  all  bridges  the  chords  which  are  con- 
nected by  the  floor  system  are  connected  by  a  horizontal  truss  system, 
also  called  the  lateral  bracing.  One  of  these  systems  is  called  the 


Stringers 


Fig.  7.    Through  Bridge,  Showing  Top  and  Bottom  Systems  of  Lateral  Bracing,  also 
Portal  Bracing  and  Floor  System. 

top  lateral  system,  as  it  connects  the  top  chords;  and  the  other  is  called 
the  bottom  lateral  system,  as  it  connects  the  bottom  chords  (see  Fig.  7). 

14.  Portals.    In  through  bridges,  the  end-posts  of  the  pair 
cf  trusses  are  connected  by  a  system  of  braces  in  order  to  preserve 
the  rectangular  cross-section  of  the  bridge.    This  is  called  the  portal 
bracing  (see  Fig.  7). 

15.  Sway  Bracing  and  Knee=Braces.    These  serve  the  same 
purpose  as  the  portal  braces,  and  are  either  small  struts  or  systems 


15 


BRIDGE  ENGINEERING 


of  cross-bracing  placed  at  the  intermediate  posts.     The  former  are 
called  knee-braces,  and  the  latter  sway  bracing. 

16.  Floor  Systems.    In   both  highway  and   railway  bridges, 
there  are  beams  running  from  the  intermediate  posts  or  hip  ver- 
ticals across  to  the  like  members  opposite.     These  are  called  floor- 
beams.     In  highway  bridges,  there  are  smaller  beams  running  parallel 
to  the  trusses  and  resting  at  their  ends  upon  the  floor-beams.     These 
are  called  floor-joists,  and  the  plank  or  other  floor  rests  directly  upon 
them.     In  railway  bridges,  two  beams  or  girders  per  track  run  parallel 
to  the  trusses  and  are  connected  at  their  ends  to  the  floor-beams. 
These  are  called  track  stringers  (or  simply  stringers).  The  ties  rest 
directly  upon  them.     The  various  members  of  the  floor  system  of 
a  railway  bridge  are  shown  in  Fig.  7.     The  diagonals  connecting  the 
top  chords,  and  those  connecting  the  bottom  chords,  are  the  top  and 
bottom  laterals  respectively. 

CLASSES  OF  TRUSSES 

17.  Names.     Trusses    may    be    classified    according    to    their 
names,  the  character  of  their  chords,  and  the  system  of  webbing. 
Table  I  gives  the  classification  of  the  more  important  of  these  accord- 
ing to  name. 

TABLE  I 
Chronological  List  of  Trusses 


ORIGIN 

King-Post 

1570 

Palladio 

Italy 

Fig.     1 

King-Post 

1798 

Theodore  Burr 

America 

Fig.     1 

Burr 

1798 

Theodore  Burr 

America 

Fig.     8 

Warren 

1838 

England 

Fig.     9 

Howe 

1840 

William  Howe 

America 

Fig.   10 

Pratt 

1844 

Thos    &  Caleb  Pratt 

America 

Fig.   11 

WThipple 
Bowstring 
Baltimore 

1847 
1847 
1877 

Squire  Whipple 
Squire  Whipple 
Penn.  R.  R. 

America 
America 
America 

Fig.  12 
Fig.  13 
Fig.  14 

Of  the  types  of  trusses  listed  in  Table  I,  the  Warren,  Howe, 
Pratt,  Bowstring,  and  Baltimore  are  now  built;  and  of  these  construc- 
tions probably  90  per  cent  are  Pratt  trusses.  The  Baltimore  truss 
is  used  for  long  spans  only. 

18.    Chord    Characteristics.     In    most    types    of    bridges    the 


16 


BRIDGE  ENGINEERING 


Fig.  8.    Burr  Truss. 


Fig.  9.  Warren  Truss. 


Fig.  10.    Howe  Truss. 


Fig.  11.    Pratt  Truss. 


Fig.  12.    Whipple  Truss. 


17 


BRIDGE  ENGINEERING 


chords  are  parallel.  When  such  is  the  case,  the  stresses  increase 
from  the  end  toward  the  center,  and  there  is  a  considerable  difference 
between  any  two  adjacent  panels  of  the  same  chord.  This  neces- 
sitates different  areas  for  each  section.  When  the  chords  are  not 
parallel,  as  in  the  bowstring  truss,  the  stresses  in  the  chords  are  so 
nearly  equal  that  the  same  area  is  used  throughout  or  nearly  through- 
out the  entire  chord.  Also,  the  stresses  in  the  diagonals  are  nearly 
equal.  These  conditions  would  seem  to  indicate  that  this  was  a  very 
economical  form  of  truss.  Theoretically  it  is;  but  practical  con- 
siderations— such  as  the  beveled  joints  and  the  posts  wrhich  must  be 
constructed  to  withstand  reversals  of  stress — customarily  limit  this 
type  to  the  longer  spans. 

19.  Web    Characteristics.    The    web    systems   of    the    Burr, 
Warren,  Howe,  Pratt,  and  Bowstring  trusses  are  called  single  sys- 
tems; that  of  the  Whipple  truss  is  a  multiple  system;  while  those  of 
the  Baltimore  trusses  are  examples  of  webbing  with  sub-systems. 
As  the  maximum  economical  panel  length  has  been  found  to  be  about 
25  feet,  which  makes  the  economical  height  of  the  truss  about  30 
feet,  and  as  the  length  of  the  span  should  not  be  more  than  ten  times 
the  depth,  the  span  for  trusses  with  simple  systems  of  webbing  is 
limited  to  about  300  feet.     In  order  to  increase  the  limiting  span, 
multiple  systems  like  that  of  the  Whipple  or  similar  ones  were  intro- 
duced.    Calculations  of  stresses  in  members  of  the  Whipple  truss  are 
somewhat  unreliable  on  account  of  the  fact  that  we  are  unable  to 
tell  just  how  the  effects  of  the  loads  are  distributed.   For  this  reason, 
that  type  has  gone  out  of  use,  and  the  sub-systems  are  used  instead. 
These  allow  spans  of  twice  the  above  limit;  and,  indeed,  trusses  with 
this  type  of  webbing  have  been  built  up  to  and  over  600  feet.     This 
style  of  webbing  can  be  applied  to  the  bowstring  truss,  almost  all 
long-span  bridges  being  of  this  type  with  sub-systems  of  webbing. 

WEIGHTS  OF  BRIDGES 

20.  Formulae.    In  order  to  obtain   the  stresses  due  to    the 
weight  of  the  structure,  the  latter  quantity  must  be  known.     As 
this  weight  can  be  determined  only  after  the  structure  has  been 
designed,  it  is  evident  that  an  assumption  as  to  the  weight  must  be 
made.    The  best  method  is  to  use  the  actual  weight  of  a  similar 
structure  of  like  span  which  has  been  built.     As  the  necessary  data 


18 


BRIDGE  ENGINEERING 


9 


for  this  is  not  always  available,  it  is  customary  to  use  formulae  to 
derive  an  approximate  weight  of  sufficient  accuracy  for  purposes  of 
computation.  Table  II  gives  some  of  the  most  reliable  formulse. 

TABLE   II 
Formulae  for  Weights  of  Bridges 


CLASS  OF  BRIDGE 

Heavy  Interurban 
Riveted 

,.,  _  Ann  i   i  o/  i  27/1  4.          hjf  1  -1-                1  I 

E  S.  Shaw 

W          DUU  ^  L.Ctl  ~r  Zi  i  U  ~\-      ^-CHil-p    '.:     r\r\fv        1 

First-Class  High- 

1               /                        1   '           \ 

way  Riveted 

w  =  300  +  l  +  22b-\  blfl  -\  I  j 

E.  S.  Shaw 

First-Class  High- 

15      \         1,000     / 

way  Pin 

w  =  34  +  226  +  O.lQbl  +  0.71 

J.A.L.Waddell 

Light  Country 
Highway 

w  =  250  +  2.51 

Author 

Railroad  Truss 

E  50 

w  =  (650  +  70 

F.  E.  Turneaure 

Railroad  Truss 

E  40 

w  =  |  (650  +  70 

F.E.  Turneaure 

Railroad  Truss    . 

E  30 

w~=  \  (650  +  70 

F  E.  Turneaure 

Railroad  Deck 

Girder  E  50 

w  =  124.0  +  12.0Z 

Author 

Railroad  Deck 

Girder  E  40 

w  =  123.5  +  10.0Z 

Author 

Railroad  Deck 

Girder  E  30 

w  =  111.0  +  8.81 

Author 

In  the  above  formulae,  w  =  Weight  of  steel  per  linear  foot  of  span; 
I  =  Length  of  span  in  feet;  b  =  Breadth  of  roadway,  including  sidewalks. 

In  using  the  formulae  of  Table  II,  remember  that  a  span  has  two  trusses. 
The  weights  for  highway  bridges  do  not  include  the  weight  of  the  wooden 
floor,  which  may  be  assumed  as  10  pounds  per  square  foot  of  floor  surface 
All  highway  bridges  have  steel  joists.  The  weights  of  railroad  spans  do  not 
include  the  weight  of  the  ties  and  rails,  which  may  be  assumed  at  400 
pounds  per  track  per  linear  foot  of  span.  If  solid  steel  floors  are  to  be  used, 
700  pounds  per  linear  foot  of  span  are  to  be  added  to  the  weights  computed 
from  the  table. 

All  the  weights  given  for  railroad  spans  are  for  single  track.  Double- 
track  truss-spans  are  about  95  per  cent'heavier;  and  double-track  girder-spans 
are  100  per  cent  heavier.  Through  girder  spans  are  about  25  per  cent  heavier 
than  deck  girder  spans;  and  through  spans  are  about  15  to  40  per  cent  heavier 
than  deck  spans. 

The  spans  on  which  Table  II  is  based  are  of  medium  steel.  Bridges 
built  of  soft  steel  or  wrought  iron  will  weigh  10  to  15  per  cent  more. 

*  The  author  is  indebted  to  the  distinguished  engineers  whose  names  appear  in 
Table  II,  for  permission  in  this  connection  to  make  use  of  the  formulae  given  opposite 
their  names. 


10 


BRIDGE  ENGINEERING 


In  order  to  give  an  idea  of  the  relative  weights  of  steel  in  different 
classes  of  bridges,  let  it  be  required  to  compute  the  dead  weight  of  a 
100-foot  span  of  each  class.  For  heaviest  highway  bridges  to  carry 
heavy  interurban  cars: 

00  ( i  +  Ym)  =  1 358  lbs- per  linear  ft- 


27  X  16 


12 


Fig.  13.    Bowstring  Truss. 


For  heavy  riveted  highway  bridges  to  carry  heavy  farm  engines: 


u  =  300  +  100  +  22  X  16  + 


16  * 


(  1  +  y^  \ 


870  Ibs.  per  linear  foot. 


Fig.  14.    Two  Forms  of  Baltimore  Trusses. 

For  heavy  pin-connected  highway,  bridges  to  carry  heavy  farm  or 
traction  engines: 

w  =  34  +22  X  16  +  0.16  X  16  X  100  +  0.7  X  100  =  710  Ibs.  per  linear  ft. 
For  light  country  highway  bridges  to  carry  100  pounds  per  square 
foot  of  floor  surface: 

w  =  250  +  2.5  X  100  =  500  Ibs.  per  linear  foot. 
If  the  total  weight  is  required,  the  weight  of  the  wooden  floor 
must  be  added.     Take,  for  example,  the  last  bridge: 


20 


BRIDGE  ENGINEERING 


11 


Weight  of  steel    =  500  X  100  =  50  000  pounds. 

"  floor    =  100  X  16     X  10  =  16000  pounds. 

Total  dead  load  =  66  000  pounds. 

The  weight  per  linear  foot  for  a  railroad  truss  bridge  of  100-foot 

span  is: 

w  =  650  +  7  X  100  =  1  350  Ibs.  per  linear  foot. 

This  is  about  the  same  as  that  for  a  heavy  interurban  bridge 
The  reason  for  this  is  that  in  addition  to  the  heavy  rolling  stock 
of  the  electric  road,  the  heavy  highway  traffic  must  be  provided  for. 
A  deck  girder  of  100-foot  span  weighs: 

w  =  124  +  12  X  100  =  1  324  Ibs.  per  linear  foot. 

21.  Actual  Weights  of  Railroad  Spans.  In  case  actual  weights 
can  be  obtained,  a  more  exact  analysis  can  be  made.  The  weights 
of  bridges  indicated  in  the  accompanying  tables  and  diagrams,  are 
based  on  actual  constructions  recently  erected.  These  bridges  rep- 
resent the  very  best  modern  practice  of  engineers  and  manufacturers 

The  weights  of  through  truss-spans  made  of  medium  steel 
and  designed  for  E  50  loading,  are  given  in  Fig.  15.  The  weights 
include  the  weight  of  the  ordinary  open  steel  floor,  and  they  also 
include  the  weight  of  the  ties  and  rails,  which  is  taken  at  400  pounds 
per  linear  foot  per  track. 

The  weight  of  steel  in  medium  steel  deck  plate-girder  spans 
designed  for  E  50  loading,  is  given  in  Table  III. 

TABLE    III 

Weights  of  Deck  Plate-Girders,  Medium  Steel 

Loading  E  50 


SPAN 
(in  feet) 

W  FIGHT 

(in  pounds) 

SPAN 
(in  feet) 

WEIGHT 
(in  pounds) 

15 

5300 

70 

59500 

20             7  800 

75 

67300 

25 

11  800 

80 

76300 

30 

14  500 

85 

94200 

35 

18800 

90 

105  500 

40 

23  300 

95 

114200 

45 

27400 

100 

123  600 

50 

32  400 

105 

146000 

55 

38  800 

110 

161  700 

60 

45  500 

115 

174  900 

65 

51  500 

120 

187000 

The  spans  are  the  distance  center  to  center  of  bearings;  and  the  weights 
do  not  include  the  weight  of  the  ties  and  rails,  which  is  to  be  taken  at  400 
pounds  per  linear  foot  per  track.  Intermediate  spans  may  be  interpolated. 


12 


BRIDGE  ENGINEERING 


22.  Actual  Weights  of  Highway  Spans.    The  actual  weights 
of  highway  spans  for  heavy  interurban  trolley-cars  and  traffic,  should 
preferably  be  computed  from  the  formulae  of  Shaw  or  Waddell  (Table 
II).  7The  weights  of  country  bridges,  including  floor,  may  be  taken 
from  the  diagram  of  Fig.  16. 

LOADS 

23.  Classes  of  Loads.    Those  weights  just  given  constitute 
what  is  called  the  dead  load  of  the  bridge.     The  traffic  which  passes 


130.000 

/ 

1 

/ 

1 
I  £0.000 

/ 

/ 

1 

MOCOO 

/ 

i 

IOQOOO 

/ 

/ 

| 
90.000 

/ 

/ 

80.000 

7 

/ 

70000 

7 

/ 

6QOOO 

/ 

1 

/ 

| 
50,000 

/ 

4-0  OOO/ 

,Pa 

n  in 

K'c 

t 

Fig.  15.    Weights  of  Through  Truss-Spans.        Fig.  16.    Weights  of  Country  Bridges,  In 
Medium  Steel,  E  50  Loading.  eluding  Floor. 

over  the  bridge  is  called  the  live  or  moving  load.  In  addition  to  the 
two  classes  mentioned,  is  the  effect  of  the  wind,  which  is  designated 
as  the  wind  load.  These  loads  vary  with  the  class  of  bridge,  be  it 
highway  or  railway,  and  with  the  purpose  for  which  it  is  intended. 

24.  Live  Loads  for  Highway  Bridges.  Highway  bridges  are 
usually  divided  into  several  classes  according  to  the  traffic,  which 
may  be  that  of  heavy  interurban  cars,  light  trolley-cars,  farm  engines, 
road  rollers,  teams,  human  beings,  or  some  combination  of  these 
loadings.  The  standard  specifications  of  J.  A.  L.  Waddell  or  of 
Theodore  Cooper  are  obtainable  for  a  very  small  sum.  Their  pur- 


BRIDGE  ENGINEERING  13 

chase  is  advised,  and  the  reader  is  referred  to  them  for  further  infor- 
mation. 

The  trusses  of  country  highway  bridges  are  usually  designed  for 
a  live  load  of  100  pounds  per  square  foot  of  roadway.  This  may  be 
considered  good  practice;  and  it  is  the  law  in  some  States.  The 
floor  system  of  these  same  bridges  should  be  of  sufficient  strength  to 
sustain  100  pounds  per  square  foot  of  roadway,  or  a  12-ton  farm 
engine  having  4  tons  on  the  two  rear  wheels,  which  are  12  inches  wide 
and  6  feet  apart,  and  2  tons  on  each  of  the  front  wheels,  which  are  6 
inches  wide  and  5  feet  apart.  The  axles  of  this  engine  are  spaced 
8  feet  center  to  center. 

25.  Live  Loads  for  Railway  Bridges.  The  loads  for  any  par- 
ticular railroad  bridge  are  not  always  the  same,  on  account  of  the 
great  variation  in  the  weights  and  wheel  spacings  of  engines  and 
cars.  It  is  customary  to  design  the  bridge  for  the  heaviest  in  use 
at  the  time  of  construction,  or  for  the  heaviest  that  could  reasonably 
be  expected  to  be  built  thereafter. 

As  the  computations  with  engines  were  formerly  somewhat 
laborious  on  account  of  the  different  weights  and  spacing  of  wheels, 
it  has  been  proposed  by  some  engineers  to  use  a  uniform  load,  called 
the  equivalent  load,  which  would  give  stresses  the  same,  or  very  nearly 
the  same,  as  those  obtained  by  the  use  of  engine  loads.  However, 
as  these  loads  are  different  for  each  weight  of  engine,  and  also  different 
for  the  chord  members,  the  web  members,  and  the  floor-beam  reaction 
of  each  different  length  of  span,  and  as  the  labor  of  the  computations, 
using  engine-wheel  loads,  has  been  greatly  reduced  by  means  of 
diagrams,  it  does  not  seem  as  if  this  method  would  ever  come  into 
very  general  favor  except  for  long-span  bridges,  where  the  live  load  is 
much  smaller  than  the  dead  load. 

The  equivalent  loads  for  Cooper's  E  40  (see  Fig.  85)  are  given 
in  Table  IV. 

Most  railways  specify  that  their  bridges  shall  be  computed  by 
using  two  engines  and  tenders  followed  by  a  train.  The  spacing 
of  the  wheels,  and  the  load  which  comes  on  each  wheel  of  the  engines 
and  tenders,  are  fixed  by  the  railway  company.  The  train  is  repre- 
sented by  a  uniform  load.  Formerly  there  was  a  great  diversity  of 
practice  among  the  different  roads  in  regard  to  the  engine  and.  train 
loads  specified ;  but  practice  has  of  late  years  become  quite  uniform, 


It 


BRIDGE  ENGINEERING 


TABLE  IV 

Equivalent  Uniform  Loads 

Loading  E  40 


SPAN 
(in  feet) 

EQUIVALENT  UNIFORM  LOAD 

SPAN 
(in  feet) 

EQUIVALENT  UNIFORM  LOAD 

Chords 

Web 

Floor- 
Beam 

Chords 

Web 

Floor- 
Beam 

10 

9000 

12  000 

8200 

46 

6330 

7240 

5240 

11 

9310 

11  640 

7960 

48 

6220 

7  140 

5200 

12 

9  340 

11  330 

7830 

50 

6  110 

•  7060 

5  140 

13 

9340 

11  080 

7600 

52 

6040 

6940 

5  130 

14 

9210 

10  860 

7  460 

54 

5960 

6820 

5  120 

15 

9030 

10  670 

7  330 

56 

5880 

6  720 

5  110 

16 

8850 

10  500 

7  120 

58 

5800 

6  620 

5090 

17 

8650 

10  350 

6940 

60 

5  730 

6530 

5080 

18 

8430 

10  240 

6780 

62 

5690 

6490 

5080 

19 

8220 

10  100 

6630 

64 

5700 

6450 

5070 

,20 

8000 

10  000 

6500 

66 

5620 

6450 

5070 

21 

8040 

9  780 

6390 

68 

5560 

6380 

5060 

22 

8040 

9  580 

6290 

70 

5510 

6340 

5060 

23 

8010 

9  400 

6200 

72 

5490 

6320 

5030 

24 

7960 

9  230 

6  120 

74 

5460 

6  300 

5010 

25 

7890 

9080 

6040 

76 

5440 

6290 

4990 

26 

7  780 

8  930 

5  970 

78 

5420 

6  270 

4970 

27 

7660 

8  790 

5900 

80 

5400 

6250 

4950 

28 

7  540 

8660 

5830 

82 

5  370 

6230 

4930 

29 

7420 

8  540 

5  770 

84 

5340 

6200 

4910 

30 

7300 

8430 

5720 

86 

5310 

6  180 

4890 

31 

7220 

8  320 

5680 

88 

5270 

6  150 

4870 

32 

7  140 

8  190 

5650 

90 

5250 

6  130 

4860 

33 

7  050 

8080 

5620 

92 

5250 

6  110 

4830 

34 

6  960 

7980 

5600 

94 

5210 

6  090 

4810 

35 

6870 

7890 

5570 

96 

5  170 

6060 

4  780 

36 

6820 

7820 

5  530 

98 

5  150 

6  040 

4  760 

37 

6760 

7750 

5  500 

100 

5  140 

6  020 

4  740 

38 

6700 

7690 

5  460 

125 

5  100 

5  770 

4  720 

39 

6630 

7630 

.  5  430 

150 

5010 

5570 

4700 

40 

6  560 

7  570 

5400 

175 

4890 

5350 

4686 

42 

6  530  j   7  450 

5  340 

200 

4740 

5240 

4660 

44 

6  470 

7340 

5300 

250 

4510 

5030 

4  640 

with  an  apparent  tendency  to  standardize  in  accordance  with  the 
classes  of  loading  specified  by  Cooper.  Cooper's  Class  E  50,  which 
represents  the  heaviest  engines  now  in  common  use,  was  invented 
by  Theodore  Cooper,  a  consulting  engineer  of  New  York  City.  It  is 
given  in  Fig.  17. 

Lighter  loadings  for  light  traffic  on  the  same  general  plan  are 
advocated  by  Mr.  Cooper,  and  are  given  at  length  in  his  "General 
Specifications  for  Iron  and  Steel  Railway  Bridges  and  Viaducts" 
(1906  edition). 

26.    Wind  Loads.     Some  designers  require  that  the  stresses  due 


24 


BRIDGE  ENGINEERING 


15 


•A 

-GH- 

~<n 

CfCFTze G  "  J~ 

ooszc     \^,  ~  Y" 

OOSZC G  H~ 


H 

:4 


0000 


ji 

*-fc 


H 


to  wind  shall  be  computed  by  using  30  pounds 
per  square  foot  of  actual  truss  surface.  This 
requires  that  you  know  the  size  of  the  mem- 
bers of  the  bridge  before  it  is  designed — which 
is  evidently  an  impossibility;  or  that  an  as- 
sumption as  to  their  size  be  made — which 
allows  a  chance  for  a  mistake  in  judgment, 
especially  in  an  inexperienced  person.  A  more 
logical  method,  and  one  used  to  a  great  extent, 
is  to  assume  a  force  of  so  many  pounds  per 
linear  foot  to  act  on  the  top  and  bottom  chords 
and  on  the  traffic  as  it  moves  across  the  bridge. 

In  highway  through  bridges,  it  is  the  usual 
practice  to  take  the  wind  load  as  150  pounds 
per  linear  foot  of  top  and  bottom  chords,  and 
150  pounds  per  linear  foot  of  the  amount  of 
live  load  which  is  on  the  bridge. 

For  railroad  bridges,  it  is  customary  to  use 
considerably  higher  values  than  those  used  in 
highway  practice — not  that  the  wind  blows 
harder  on  railroad  than  on  highway  bridges, 
but  so  that  the  bracing  designed  by  the  use  of 
these  values  may  be  sufficiently  strong  to  stiffen- 
the  bridge  not  only  against  the  wind,  but  also 
against  the  vibrations  caused  by  the  rapidly 
moving  traffic.  Good  practice  for  through 
bridges  is  to  use  150  pounds  per  linear  foot 
of  the  top  chord,  150  pounds  per  linear  foot 
of  the  bottom  chord,  and  450  pounds  per  linear 
foot  of  live  load  on  the  bridge.  This  latter 
force  is  supposed  to  act  at  a  line  8.5  feet  above 
the  base  of  the  rail. 

For  deck  bridges,  for  both  highway  and 
railway  use,  the  unit-loads  on  the  moving  or  live 
load  remain  the  same,  but  the  unit-loads  on 
the  top  and  bottom  chords  are  reversed. 

In  computations  involving  the  live  load,  it 
is  always  assumed  that  the  live  load  moves  over 
the  bridge  from  right  to  left. 


OOOQ2 (^        f 

N  I 


!^i 
K-e4 


OOOC 


"5~\^  HT 

\~/ 


_ 

oodog  \^  ~T 


\ 


1 1 

3  I 

8  « 

(J  M 


25 


1(5 


BRIDGE  ENGINEERING 


THEORY 

27.     Principles  of  Analysis.    The  stresses  in  bridge  trusses  may 
be  determined  by  both  algebraic  and  graphic  methods.     In  some 


Fig.  18.    Truss  under  Loads,  Illustrating  Principles  of  Analysis. 

cases,  one  is  more  expeditious  than  the  other.     Algebraic  methods 
alone  will  be  considered  in  this  text. 

The  analysis  of  stresses  is  based  upon  the  fact  that  the  interior 
stresses  in  a  member  or  group  of  members  hold  in  equilibrium  the 
exterior  forces.  That  this  is  a  fact,  can  easily  be  understood.  Con- 
sider a  man  pulling  on  a  rope  which  is  fastened  at  one  end  to  an  im- 
movable object.  There  will  be  a 
stress  in  the  rope  equal  to,  and 
opposite  in  direction  to,  the  pull 
exerted  by  the  man.  In  order  to 
prove  this,  cut  the  rope  and  ap- 
ply a  force  equal  and  opposite  to 
the  pull  exerted  by  the  man,  where 
the  cut  is  made;  and  the  rope 
and  man  will  be  in  equilibrium. 
Also,  suppose  that  a  truss  under 
loads,  as  indicated  by  the  arrows, 
Fig.  18,  were  cut  along  the  section 
a-a,  and  that  forces  Fv  F3,  F5 
equal  to  the  stresses  S2,  S3,  and  S5  were  placed  at  the  ends  of  the 
members  as  indicated  in  Fig.  19,  then  that  portion  of  the  truss  to 
the  left  of  the  section  would  be  in  equilibrium.  The  interior  stresses, 
represented  by  F2,  F3,  and  F5,  would  hold  in  equilibrium  the  exterior 
forces  p  and  R, 


Forces  Substituted  for  Stresses  in 
Truss  of  Fig.  18. 


26 


BRIDGE  ENGINEERING 


17 


From  inspection  of  Fig.  19,  it  will  appear  evident  that,  as  the 
position  of  the  truss  to  the  left  of  the  section  is  in  equilibrium,  the 
following  statements  are  true : 

1.  The  algebraic  sum  of  the  moments  of  the  exterior  forces  and  the 
stresses  in  the  members  cut  by  the  section,  is  equal  to  zero.  This  is  true  of  the 
moments  taken  about  any  or  all  points;  for,  if  it  were  not,  the  portion  of  the 
truss  would  begin  to  rotate  about  some  point,  and  would  continue  until 
equilibrium  was  established. 

2.  In  a  vertical  plane,  the  algebraic  sum  of  the  components  of  the 
exterior  forces  and  the  stresses  in  the  members  cut  by  the  section  is  equal 
to  zero;  for,  if  such  were  not  the  case,  the  portion  of  the  truss  shown  would 
move  up  or  down  with  a  constant  acceleration. 

3.  The  algebraic  sum  of  the  components  of  the  exterior  forces  and  the 
stresses  in  the  members  cut  by  the  section  in  a  horizontal  plane,  is  equal  to 
zero;  for,  if  such  were  not  the  case,  the  portion  of  the  truss  would  move  either 
to  the  right  or  to  the  left,  with  a  constant  acceleration. 

4.  From  2  and  3,  above,  it  is  evident  that  the  algebraic  sum  of  the 
components  of  the  exterior  forces  and  the  stresses  in  the  members  cut  by 
the  section  is  equal  to  zero  in  any  and  all  planes. 

The  section  is  not  necessarily  required  to  be  a  vertical  line  as  in 


P     b 


Pig.  20. 

Oblique  Section  Cutting 
Truss. 


Fig.  20a. 

Circular  Section 
Cutting  Truss. 


Fig.  21. 

Illustrating  Resolution 
of  Forces. 


Fig.  19.  It  may  be  oblique,  as  in  Fig.  20;  or  it  may  be  a  circular 
section,  as  shown  in  Fig.  20a.  When  the  latter  is  the  case,  it  is  said 
that  the  sum  of  the  components  of  the  forces  around  the  point  Ut 
is  in  equilibrium  in  any  plane  that  may  be  taken. 

It  is  also  evident  that  the  forces  in  the  members  cut  by  the 
section,  and  the  exterior  forces  to  the  right,  are  in  equilibrium. 
This  condition  is  very  seldom  utilized  in  the  determination  of  stresses, 
as  that  portion  of  the  truss  to  the  left  of  the  section  is  almost  always 
considered. 

28.     Resolution  of  Forces.    This  method  is  one  of  the  simplest 


27 


is 


BRIDGE  ENGINEERING 


and  at  the  same  time  least  laborious.  The  forces  are  generally 
resolved  into  their  horizontal  and  vertical  components,  or  parallel 
and  perpendicular  to  some  member.  In  cases  where  two  unknown 
stresses  occur,  two  equations  can  usually  be  formed,  and  these  solved. 
It  should  be  assumed  that  the  unknown  stress  acts  away  from 
the  section  which  cuts  it.  It  will  then  solve  out,  with  the  proper 
sign  indicating  the  character  of  the  stress — that  is,  whether  it  is 
tensile  or  compressive.  Tensile  stresses  are  indicated  by  placing 


Diagrams  Illustrating  Application  of  Method  of  Resolution  of  Forces  in  Analysis  of 
Trusses. 

the  plus  (+)  sign  before  them,  while  a  minus  (  — )  sign  indicates 
compression. 

A  few  equations  showing  the  application  of  the  method  of  the 
resolution  of  forces  can  be  written  after  inspection  of  Figs.  21  to  25 
inclusive.  In  all  cases,  <SX  is  the  unknown  stress,  and  is  assumed 
to  be  acting  away  from  the  section.  The  other  stresses  Slt  S2,  etc., 
are  known,  and  their  direction  given  them  accordingly,  it  being 
toward  the  section  if  the  member  is  in  compression,  and  away  from 
the  section  if  the  member  is  in  tension.  Forces  or  components 
acting  upward  or  to  the  right  are  considered  plus ;  those  acting  down- 


BRIDGE  ENGINEERING  19 

ward  or  to  the  left  are  considered  minus.    For  a  fuller  explanation, 
see  the  instruction  paper  on  Statics,  Articles  17  to  23  inclusive. 

In  Fig  21,  the  sum  of  the  vertical  components  is  taken,  and  the 

equation  is : 

+  R  -  p  —  p  -  Sx  cos  $  =  0; 
whence, 

Sx  =   -  (  +  R-p  -  p)  sec  0. 

In  Fig.  22,  the  section  is  oblique,  and  the  sum  of  the  vertical 
components  is  taken : 

+  R  -  p  -  p  +  SK  =  0; 
whence, 

S»  -  -  (  +  R  -  p  -  p). 

In  both  of  the  above  cases,  it  will  be  noted  that  the  chord 
stresses  do  not  enter  into  the  equation,  as  their  vertical  components 
are  zero. 

In  Fig.  23,  the  sum  of  the  horizontal  forces  is  used  in  deter- 
mining the  stress  Sx.  Note  that  the  exterior  forces  R  and  p  do  not 
enter  the  equation,  as  they  are  not  to  the  left  of  the  section,  and  also 
their  horizontal  components  are  zero. 

+  Sl  sin  0  +  S2  sin  0  +  S3  sin  <£  +  S*  =  0; 
whence, 

5X  =   -  (Sl  +  S2  +  S3)  sin  (f>. 

In  Fig.  24,  the  sum  of  the  vertical  forces  is  again  used.  Here 
the  section  cuts  the  member  with  the  known  tensile  stress  Sr 

+  R  —  p  —  p  —  p  —  p  —  P  +  Si  cos  <j)  —  >SX  cos  <j6  =  0; 
whence, 

Sx  =   +  (R  -  5p)  sec  $  +  Si. 

In  Fig.  25,  use  is  made  of  the  fact  that  the  sum  of  the  components 
of  the  forces  about  a  point  is  zero  when  they  are  resolved  in  any  plane. 
Here  they  will  be  resolved  perpendicular  to  the  diagonal. 

-Si  sin    $+  Sx  =  0. 

Sx  =   +Sisin  <£. 

These  are  some  of  the  most  common  cases  which  occur  in  the 
determination  of  stresses  in  simple  trusses.  In  all  cases,  follow  this 
method  of  procedure: 

1.  Pass  a  section  cutting  as  few  members   as  possible,  one  of  which 
must  be  the  one  whose  stress  is  desired. 

2.  The  stress  in  all  the  members  cut,  with  but  one  exception,  must  be 
known. 

3.  Write  your  equation,  always  placing  it  equal  to  zero. 

4.  Solve  for  your  stress. 


29 


20 


BRIDGE  ENGINEERING 


29.  Method  of  Moments.  The  stresses  in  all  members  of  a 
truss  can  be  determined  by  this  method.  By  section  1  of  Art.  28, 
the  point  about  which  the  moments  are  considered  can  be  taken 
anywhere.  Fig.  26  represents  the  point  as  taken  somewhere  outside 
of  the  truss  at  a  distance  a  above  the  point  U  r  The  equation  will 

then  be : 

-  S,  X  a  -  S2  X  b  -  S3  (a  +  h)  +  Rp  ±  P,  X  0  +  P2  X  p  =  0. 
This  involves  three  unknown  quantities,  and   therefore   two  other 
r-    cm  points  should  be  taken,  and  two 

"^r  more  equations  written.     By  the 

use  of  the  three  equations,   the 
stresses  can  be  determined. 

It  is  customary  to  assume  the 
center  of  moments  at  such  a  place 
th&t  the  moments  of  all  the  un- 
known stresses,  wTith  one  excep- 
tion, are  zero.  This  condition 
requires  that  their  lines  of  action 
pass  through  the  center  of  mo- 
ments. Let  it  be  required  to 
53  determine  the  stress  S3.  If  the 
center  of  moments  is  taken  at 
Uv  then,  as  the  lines  of  action 
of  Sl  and  S2  pass  through  this 


point,  their  moments  will  be  zero, 
and  the  following  is  true: 
+  R  X  2p  -  P,  X  p  ±  P2  X  0  -  S3  X  K  =  0. 


Fig  26.    Diagram  Illustrating  Application 

of  Method  of  Moments  in  Analysis 

of  Trusses. 


whence, 


-i-  (  +  R  X2p  - 


Likewise,  if  the  top  chord  is  curved,  the  center  of  moments  can  be 
taken  in  such  a  position  that  only  tiie  unknown  stress  will  enter  into 
the  equation.  If  it  is  desired  to  determine  the  stress  <S2,  Fig.  27, 
the  equation  would  be: 

-  S2  X  I  -  R  X  a  +  PJ  (a  +  p)  +  P2  (a  +  2p)  =  0, 
the  center  of  moment  being  atO,  the  intersection  of  the  lines  of  stress 
of  (Sj  and  S3.     Solving  the  equation  just  stated, 

S2  =  -y  j  -Ra  +  P,  (a  +  p)  +  P2  (a    +   2p)    1 


30 


BRIDGE  ENGINEERING 


21 


30.  Stresses  in  Web  Members.  By  reference  to  Articles  28  and 
29,  it  is  seen  that  several  methods  are  presented  for  the  solution  of 
stresses  in  web  members.  Each  should  be  adapted  to  the  case  in 
hand.  The  simplest  method,  and  the  one  which  is  commonly  used 
in  all  trusses  with  parallel  chords,  is  by  the  resolution  of  the  vertical 
forces.  Fig.  21  is  to  be  referred  to.  The  equation  given  on  page 

19  is: 

+  R  -  p  —  p  -  Sx  cos  <£  =  0. 


Fig.  27.    Diagram  Illustrating  Application  of  Method  of  Moments  In  Analysis  of  Trusses. 
Top  chord  curved.    . 

But  R  —  p  —  p  is  equal  to  V,  the  vertical  shear  at  the  section,  and 
so  the  equation  may  now  be  written : 

V  -  Sxcos  0  =0 (1) 

whence  the  following  important  rule  is  deduced: 

'The  algebraic  sum  of  the  vertical  shear  at  the  section  and  the  ver- 
tical components  of  the  stress  in  all  of  the  members  cut  by  the  section,  is 
equal  to  zero. 

In  trusses  with  horizontal  chords  and  a  simple  system  of  webbing, 
the  equation  may  be  put  in  the  form : 

SK    =  +  V  sec  <£; 

and  the  statement  that  the  stress  in  any  web  member  is  equal  to  the 
shear  times  the  secant  of  the  angle  that  it  makes  with  the  vertical  is 


31 


22 


BRIDGE  ENGINEERING 


true.  The  practice  of  using  this  latter  statement  is  not  to  be  en- 
couraged, as  it  leads  to  confusion  in  the  signs  of  the  stresses.  Equa- 
tion (1 )  should  be  written  in  all  cases,  and  the  stress  will  then  solve  with 
its  correct  characteristic  sign,  indicating  that  the  stress  is  either 
tensile  or  compressive. 

As  an  example,  let  it  be  required  to  determine  the  stresses  in  the 
web  members  S2  and  S3  of  the  Pratt  truss  shown  in  Fig.  28,  the  loads 
being  in  thousands  of  pounds.  First,  a  section  should  be  passed, 
cutting  that  member  and  as  few  others  as  possible.  Next,  the  shear 
at  that  section  should  be  computed.  Then  the  vertical  components 
of  all  the  stresses  cut  by  the  section,  and  the  vertical  shear,  should  be 


Fig.  28.    Calculation  of  Stresses  in  Web  Members  of  Pratt  Truss. 

equated  to  zero.      Finally,  solve  the  equation.      Remember  that  the 
unknown  stress  is  to  be  assumed  as  acting  away  from  the    section, 
and  that  forces  or  resultants  acting  downward  are  considered  negative, 
while  those  acting  upward  are  considered  positive. 
To  determine  S2: 

The  vertical  shear  at  the  section  a—  a  is : 

+  37.5  -  2  X  10  -  5  =   +12.5. 
As  the  chord  stresses  do  not  exert  a  vertical  component,  the  equation  is : 

+  12.5  +  S2  =  0 

S2  =   —12.5,  which  is  a  compressive  stress  of  12,500  pounds. 
Note  that  in  this  case  the  angle  which  the  member  makes  with  the 
vertical  is  zero,  and  the  cosine  and  secant  are  unity. 
To  determine  S3: 

The  vertical  shear  at  the  section  b  —  b  is 

+  37.5  -2X10-2X5=   +7.5. 
The  equation  is: 

+  7.5  -  S3  cos  4>  =  0 

Ss  =  +7.5-S6C  <£. 


BRIDGE  ENGINEERING 


23 


Sec  0  is  equal   to   VW  +  252  -h  30,  which  is  equal  to  1.302;  and 
therefore, 

S3  =   +7.5  X  1.302 

=   +9.765,  which  is  a  tensile  stress  of  9,765  pounds. 

31.  Stresses  in  Chord  Members.  The  stresses  in  chord  may  be 
obtained  by  either  the  method  of  moments  or  the  method  of  resolu- 
tion of  forces,  this  latter  being  usually  the  resolution  of  horizontal 
forces. 

In  accordance  with  the  text  of  Article  29,  the  following  rule  may 
be  stated  with  regard  to  the  solution  of  stresses  in  chord  members 
by  the  method  of  moments: 

Pass  a  plane  section  cutting  the  member  whose  stress  is  to  be  computed, 
and  as  few  others  as  possible;  then  take  the  center  of  moments  at  such  a  point 


s< 


t' 

t 

/ 

/ 

/ 

/ 

/' 

/ 

\ 

1 

>' 

/  ' 

Fig.  29.    Calculation  of  Stresses  iu  Chord  Members  by  "Tangent"  or  "Chord-Increment" 

Method. 

that  the  lines  of  action  of  as  many  forces  as  possible,  the  unknown  one  excepted, 
pass  through  that  point;  write  an  equation  of  the  moments  about  this  point  of 
the  known  loads  and  forces  to  the  left  of  the  section,  assuming  the  unknown  force 
to  act  away  from  the  section,  and  taking  the  known  forces  to  act  as  given,  the 
tensile  stresses  to  act  away  from  the  section,  and  the  compressive  stresses  to  act 
towards  the  section;  place  the  equation  equal  to  zero,  and  solve. 

The  stress  will  solve  out  with  its  correct  characteristic  sign. 

In  the  majority  of  cases  a  section  can  be  made  to  cut  three  mem- 
bers only,  one  of  the  three  being  the  one  whose  unknown  stress  is 
desired.  In  such  cases,  take  the  center  of  moments  at  the  inter- 
section of  the  other  two,  and  proceed  as  before.  As  examples  of  this 
latter  case,  note  the  centers  of  moments  at  U2,  Fig.  26,  and  0,  Fig. 
27,  and  also  the  equations  resulting  therefrom. 

When  the  method  of  resolution  of  forces  is  used,  it  is  usually 
designated  as  the  tangent  method  or  the  chord  increment  method.  The 
simplest  application  of  this  method  is  to  trusses  with  horizontal 
chords  and  vertical  posts  in  the  web  members.  Then  the  stress  in 
any  chord  member  is  equal  to  the  product  of  the  sum  of  the  shears 


33 


24 


BRIDGE  ENGINEERING 


in  the  panels  up  to  that  section,  and  the  tangent  .of  the  angle  which 
the  diagonals  make  with  the  vertical. 

This  can  readily  be  proved  by  reference  to  Fig.  29.  Let  it  be  re- 
quired to  determine  the  stress  in  the  chord  member  SK,  Pass  the 
section  a— a.  The  stresses  Sv  Sv  S3,  and  St  are  now  computed, 
and  are  Sj=  —  Vl  sec  <f>;  S2=  +  T7",  sec  9;  S3  =  +TT3  sec  9;  and  S4  = 
+  F4sec  9.  Now  noting  the  directions  of  the  known  stresses  and 


Lo  L,'  Le  L=>  L«.  L5  L6 

Fig.  30.    Illustrating  Method  of  Notation  of  Stresses  and  Members  in  a  Through  Bridge. 


L.  Le  L3  L4  L5 

Fig.  31.    Illustrating  Method  of  Notation  of  Stresses  and  Members  in  a  Deck  Bridge, 

assuming  S,  to  act  away  from  the  section,  the  equation  of  the  hori- 
zontal component  is: 

4-  Sl  sin  $  +  Sj  sin  $  +  S,  sin  <j>  +  St  sin  ij>  +  S,    =  0. 
Now,  substituting  the  values  of  Sv  Sv  etc.,  and  remembering  that 


sec  <    = 


COS   <f> 

•  '-•; 

from  which,  - 


.  the  equation  becomes  : 


•  7.= 


&  =  -  (F,  4-  V,  +  Vs  +  VJ  tan  0; 
Sx    =  -2Ttan  ^. 

From  inspection  of  Fig.  29,  it  will  be  noticed  that  the  stress  in 
any  section  of  the  chord  is  equal  to  that  in  the  section  to  the  left  of 


BRIDGE  ENGINEERING 


25 


it,  plus  the  increment  (horizontal  component)  of  the  diagonal;  hence 
the  name  chord  increment  method. 

32.  Notation.  The  practice  hitherto  used  in  designating 
stresses  by  Sv  S2,  etc.,  will  now  be  discontinued,  as  it  is  inconvenient 
in  the  extreme;  moreover,  it  is  not  the  method  used  in  practical  work. 
The  notation  to  be  used  is  that  given  in  Figs.  30  and  31,  the  former 
being  for  a  through  and  the  latter  for  a  deck  truss. 

The  practical  advantages  of  this  system  are  very  great.  When 
Ul  U2  is  noted,  it  is  at  once  known  to  be  the  top  chord  of 
the  second  panel;  U2  L2  is  known  to  be  the  second  vertical ;  while  U2 
L3  is  at  once  recognized  as  the  diagonal  in  the  third  panel.  A  stress 
in  a  member,  as  well  as  the  member  itself,  is  designated  by  the 
subscript  letters  at  its  ends.  Thus  Ul  L2  may  mean  the  member 


U5 


ua 


Fig.  32.    Calculation  of  Stresses  in  a  Six-Panel  Warren  Truss  Through  Bridge. 

itself  or  the  stress  in  the  member.  The  text  will  clear  this  up.  In 
analysis,  the  stress  would  be  implied,  while  in  design  the  member 
itself  would  be  intended. 

33.  Warren  Truss  under  Dead  Loads.  The  Warren  truss  has 
its  web  members  so  built  of  angles  and  plates  or  of  channels,  that 
they  can  take  either  tension  or  compression.  The  top  chord  is  of 
structural  shapes,  while  the  lower  chord  may  be  of  built-up  shapes 
or  simply  of  bars. 

Let  it  be  required  to  determine  all  of  the  stresses  in  the  six- 
panel  truss  of  a  through  Warren  highway  120-foot  span  for  country 
traffic.  The  height  is  to  be  20  feet.  The  outline  is  given  in  Fig.  32. 
According  to  Fig.  16,  the  total  weight  of  the  span,  including  wooden 
floor,  is  76  000  pounds.  Each  truss  carries  one-half  of  this,  or  76  000 


35 


26  BRIDGE  ENGINEERING 

-r-  2  =  38  000  pounds.  As  there  are  six  panels,  each  panel  load  is 
38  000  -=-  6  =  6  333  pounds.  This  means  that  we  must  compute 
the  stresses  in  the  above  truss  by  considering  that  a  load  of  6  333 
pounds  is  at  points  Lv  L2,  Z/3,  L4,  and  L5.  Of  course  there  is  some 
weight  at  L0  and  L6;  but  this  does  not  stress  the  bridge,  as  it  is 
directed  over  the  abutments  or  supports.  The  reactions  at  L0  and 
L6  are  each  equal  to  (5  X  6  333)  -T-  2  =  15  833  pounds. 
The  shears  are  next  computed,  and  are: 

F,  =  + 15  833  -  0  =  +15  833 

F2  =   +15  833  -  6  333  =   +9  500 

F3  =  + 15  833  -  2  X  6  333  =   +  3  167 

It  is  unnecessary  to  go  past  the  center  of  the  bridge,  as  it  is  symmetri- 
cal. The  Vl  represents  the  shear  on  any  section  between  Z/0  and  it; 
F2  represents  the  shear  on  any  section  between  Ll  and  L2;  and  Vs 
represents  the  shear  on  any  section  between  L2  and  L3.  The  secant 
of  the  angle  </>  is : 


(20%  10)2)  -  20=  1.12. 


The  stresses  in  the  web  members  are  computed  as  follows: 
For  L()  Ur     Pass  section  a— a.     Assume  stress  acting  away  from 
the  section,  as  shown.     Then, 

F,  +  L0Ul  cos  <£  =  0; 

L0Ul  =   -  F,  sec  <f>; 

L0U,  =  -  15  833  X  1.12  =  -  17  700  pounds, 

which  shows  that  L0  Ul  has  a  compressive  stress  of  17  700  pounds. 
For  Ul  Lv     Pass  section  6  —  6.     Assume  stress  acting  away  from 
the  section,  as  shown.     Then, 

F,  -  UtL,  cos  <£  =  0; 

U,L,  =   +'F,  sec  <£; 

tfjL,  =   +15833  X  1.12  =  +  17  700  pounds, 

which  shows  that  U^  has  a  tensile  stress  of  17  700  pounds. 
For  LJJr     Pass  section  c  —  c.     Then, 

F2-  +  L,U2cos  0  =  0; 

L,U2  =  -F2sec  $; 

L,E7,  =   -  9500  X  1.12  =   - 10  640  pounds. 

For  U2Lr     Pass  section  d-d.     Then, 

+  9500  -  U2L2cos  0  =  0; 

UgLf  =  +9500  X  1.13'-  +10640.     '    • 


BRIDGE  ENGINEERING  27 

Far  L2U3.     Pass  section  e  —  e.     Then, 

+  3  167  +  L2U3cos<t>  =  0; 

L2U3  =   -3  167  X  1.12  =   -3  540. 

For  U3L3.     Pass  section  /  —  /  .    Then, 

+  3  167  -  U3L3cos  <£  =  0; 

U3L3  =   +3  167  X  1.12  =   +3540. 

The  computation  of  the  stresses  in  the  chords  is  made  by  the 
method  of  moments,  and  is  as  follows: 

For  LULV  Section  b  —  b  cuts  UlLl  and  UJJ2,  besides  the  mem- 
ber whose  stress  is  desired,  and  therefore  the  center  of  moments  will 
be  taken  at  their  intersection  U^  The  equation  is: 

+ 15  833  X  10  -  L0L,  X  20  =  0, 
whence, 

L0L,  =  (  +  15833  X  10)  4-  20; 

=    +  7  917  =  a  tension  of  7  917  pounds. 

For  LJjr     Either  section  c  —  c  or  d  —  d  may  be  used,  and  each 
shows  the  center  of  moments  to  be  at  Uy     The  equation  is: 
+ 15  833  X  30  -  6  333  X  10  -  L,L2  X  20  =  0; 
L^  =  (  +  15  833  X  30  -  6  333  X  10)  4-  20; 

=   +20  583  =  a  tensile  stress  of  20  583  pounds. 

For  L2L3.  Either  section  e  —  e  or  /  —  /  may  be  used,  and  each 
shows  the  center  of  moments  to  be  at  Ur  The  equation  is: 

+ 15  833  X  50  -  6  333  X  30  -  6  333  X  10  -  L2L3  X  20  =  0; 

whence, 

L2L3  =   +26917. 

The  center  of  moments  for  UfJ^  is  at  Lt;  for  U2U3,  it  is  at  L2;  and 
for  UaU4,  it  is  at  L3.     The  following  equations  can  now  be  written : 

+  20  X  U,U2  +  20  X  15833  =  6;  whence  U,U2  =   -15833; 
+  20  X  U2U3  +  40  X  15  833  -  20  X  6  333  =  0;  whence  U2U'3  =   -25  333; 
+  20  X  17,174  +  60  X  15  833  -  40  X  6  333  -  20  X  6  333  =  0;  whence  U3U4 
=   -28500. 

A  diagram  of  half  of  the  truss  should  now  be  made,  and  all  the 
stresses  placed  upon  it.  The  dimensions  should  also  be  put  upon  this 
diagram.  The  student  should  cultivate  this  habit,  as  it  shows  him 
at  a  glance  the  general  relation  of  stresses  and  the  general  rules  of  their 
variations.  Fig.  33  gives  the  half-truss,  together  with  the  stresses 
and  dimensions.  The  stresses  in  the  members  of  the  right  half  of 
the  truss  are  the  same  as  those  in  the  corresponding  members  of  the 
left  half. 


37 


28 


BRIDGE  ENGINEERING 


From  inspection  of  the  above  diagram,  it  is  seen  that  the  chord 
stresses  increase  from  the  end  toward  the  center;  that  the  web  stresses 
decrease  from  the  end  toward  the  center;  and  that  all  members  slant- 
ing the  same  way  as  the  end-post  L^Jl  have  stresses  of  that  sign, 


Fig.  33.    Dimensions  and  Stress  Diagram  of  Half  a  Six-Panel  Warren  Through  Truss. 

while  all  that  slant  a  different  way  have  an  opposite  sign.  These 
relations  are  true  of  all  trusses  with  parallel  chords  and  simple  systems 
of  webbings. 

34.  Position  of  Live  Load  for  Maximum  Positive  and  Negative 
Shears.  The  dead  load,  by  reason  of  its  nature,  is  an  unchangeable 
load.  The  stresses  due  to  it  are  the  same  at  any  and  at  all  times. 


"1 

^+y  ) 

<            -y             > 

e 

W  Ibs.  per  lin.  Foot. 

Y 

*                         I                                                       r 

ft                                                                                                    * 

Fig.  34.    Calculating  Maximum  Positive  and  Negative  Shears  in  Simple  Beam  under  Live 
Load.    Conventional  Method. 

With  the  live  load,  the  case  is  different.  The  live  load  represents 
the  movement  of  traffic  upon  the  bridge.  At  certain  times  there  may 
be  none  on  the  bridge,  while  at  other  times  it  may  fill  the  bridge 
partially  or  entirely.  In  such  cases  the  shears  due  to  live  load  will  vary. 


38 


BRIDGE  ENGINEERING  29 

Conventional  Method.  It  has  been  found  that  the  maximum 
positive  shear  at  any  section  of  a  simple  beam  occurs  when  the  beam  is 
loaded  from  that  section  to  the  right  support,  and  that  the  maximum 
negative  shear  occurs  at  the  same  section  when  this  beam  is  loaded  from 
the  section  to  the  left  support.  This  can  be  proved  as  follows : 

Let  a  beam  be  as  in  Fig.  34,  and  let  a  —  a  be  the  section  under 
consideration.  The  reaction  Rl  is  due  to  the  load  wy  on  the  part  y, 
and  to  the  load  wx  on  the  part  x.  That  is, 


Now  the  shear  at  the  section  a  —  a  is  7?t  —  wx-,  or, 

'2\J~WX=Vc 

* 


w  x 


21 

/ 

X 


T' 

From  inspection  of  this  last  equation,  it  is  seen  that  wo;  ^ -, 

is  the  amount  that  is  added  to  the  reaction  by  loading  the  part  x. 
x 

~2~y 

Also.,  that -j is  less  than  unity,  is  evident.     The  amount  in 

brackets  in  the  last  equation  represents  the  effect  of  the  loading  of 
the  segment  x  of  the  beam.  As  this  is  negative  and  will  only  reduce 

the  positive  valued  term— -^  ,  it  is  therefore  proved  that  to  get  the 

largest  positive  shear  the  beam  should  be  loaded  from  the  section  to 
the  right  support. 

From  further  inspection  of  the  equation,  it  will  be  seen  that  the 
term  in  brackets,  which  represents  the  effect  of  the  load  on  the  seg- 
ment x  on  the  shear,  is  always  negative;  and  that  the  term — —  ,which 

represents  the  effect  of  the  load  on  the  segment  y  on  the  shear,  is 
always  positive.  Hence,  to  get  the  largest  negative  shear  at  the 
section,  the  load  should  be  on  the  segment  x.  That  is,  the  loading 
should  be  from  the  section  to  the  left  support. 


30 


BRIDGE  ENGINEERING 


In  a  truss,  the  loads  are  placed  at  the  panel  points;  and  the 
above  rules  in  application,  should  be  formulated  as  follows: 

To  get  the  maximum  positive  shear  at  a  section  or  in  a  panel,  load  all 
panel  points  to  the  right  of  it. 

To  get  the  maximum  negative  shear  at  a  section  or  in  a  panvl,  load  all 
panel  points  to  the  left  of  it. 

Example.  Determine  the  maximum  positive  and  the  maximum 
negative  shears  in  the  panels  of  the  7-panel  Pratt  truss  shown  in  Fig.  35,  the 


Fig.  35.    Calculation  of  Shears  in  Panels  of  7- Panel  Pratt  Truss. 


live  panel  load  being  40  000  pounds, 
the  truss  is  not  required.) 


(It  will  be  noticed  that  the  height  of 


For  maximum  +  V  in  1st  panel,  load  Lu  L2,  L3,  L4,  L5  and  L6. 


+  V 

+  v 
+  v 
+  v 
+  v 
+  v 


2d 
3d 
4th 
5th 
6th 
7th 


' '  L2,  L3,  L4,  L5,  and  L6. 

' '  L3,  L4,  Ls,  and  L6. 

"  L4,  L5,  and  L6. 

' '  L5  and  L6 

"  L6. 

"  no  panel  points  at  all. 


The  reaction  produced  by  each  of  the  loadings  is  equal  to  the 
shear  for  that  particular  case,  since  the  shear  at  any  section  or  in  any 
panel  is  equal  to  the  reaction  minus  the  loads  to  the  left  of  the  section 
or  panel,  and,  according  to  the  method  of  loading,  there  are  no  loads 
to  the  left  of  the  section ;  therefore  the  reaction  is  equal  to  the  shear. 

For  the  first  panel,  the  computation  is  made  as  follows,  the 
center  of  moments  being,  of  course,  at  L7: 

(72,  =   +  V,)  X  7  X  20  =  40  X  20  +  40  X  2  X  20  +  40  X  3  X  20  +  40  X 
4  X  20  +  40  X  5  X  20  +  40  X  6  X  20. 

It  will  be  seen  that  as  20  occurs  in  all  terms  of  this  equation,  it 
can  be  factored  out  by  dividing  both  sides  by  20,  and  the  result  will 
be  the  same.  The  equation  can  now  be  written: 


40 


BRIDGE  ENGINEERING  31 

+  V,  X  7  =  40  +  40  X  2  +  40  X  3  +  40  X  4  +  40  X  5  +  40  X  6, 
and  can  still  be  simplified  by  writing: 

+  Vl  =-—  (1+2  +  3  +  4  +  5+6)=+  120.00, 

which  is  the  form  customarily  used,  the  panel  length  being  taken  as 
a  unit  of  measurement.  The  other  shears  are  now  easily  computed 
in  a  similar  manner: 

+  va  =  -^  (1  +  2  +  3  +  4+5)=+  85.71 

+  F3  =  lP_(l  +  2  +  3  +  4)  =   +  57.14 

40 
+  V<  =  ~  (1  +  2  +  3)  =   +34.28 

40 

+  F5  =  --  (1  +  2)  =   +17.14 

+  FB  =  1°  (1)  =   +5.71 
+  V7  =  ^.(0)  -.  +0 

In  computing  the  maximum  negative  shears,  sometimes  called 
the  minimum  shears,  the  reaction  is  not  the  same  as  the  shear,  as 
there  are  loads  to  the  left  of  the  section,  and  these  must  be  sub- 
tracted. The  loadings  are: 

For  maximum  —  V  in  1st  panel,  load  no  points. 

"  L,. 

"Li  anc!L2. 
"  L,,  L2I  andL3. 
"  Llf  L2,  L3,  andL4. 
"  L,,  L,,  L3,  L4>  and  L5. 
"  L1(  L,,  L3)  L4,  Ls,  and  Lc. 

It  is  evident  that  the  maximum  —  F1  is  equal  to  zero,  there 
being  no  loads  on  the  span.  The  maximum  negative  shear  in  the 
second  panel  is  equal  to  the  reaction  produced  by  loading  the  panel 
point  Lv  and  the  load  at  i1.  Thus, 

7R,  =  40  X  6 


-  V2  =  R,  -  load  at   L, 


41 


32 


BRIDGE  ENGINEERING 


The  other  shears  are  next  computed  as  follows: 

_  V3  =  ~  (6  +  5)  -  2  X  40  =   -  17.14       . 

40 
-  V.  =  —  (6  +  5  +  4)  -  3  X  40  =  -34.28 


-57.14 


=   -  85.71 


40 


-  F7  =       -  (6  +  5  +  4  +  3  +  2+  1)-6X  40  =    -  120.00 
7 

The  maximum  positive  and  the  maximum  negative  live-load 
shears  should  now  be  written  side  by  side,  and  inspected,  in  order  to 
observe  any  existing  relations  which  might  help  to  lessen  the  labor 
of  future  computations.  The  values  are  given  in  thousands  of  pounds 
below  : 


LOCATION 

MAX.  +  LIVE-LOAD  SHEAR 

MAX.  —  LIVE-LOAD  SHEAR 

F, 

+  120.00 

-    0.00 

v, 

+  85.71 

-   5.71 

vl 

+  57.14 

-17.14 

v< 

+  34.28 

-34.28 

V, 

+  17.14 

-57.14 

V, 

+  5.71 

-85.71 

V7 

+  0.00 

-120.00 

It  is  at  once  seen  that  the  negative  shears  are  numerically  equal  in 
value  to  the  positive  ones,  but  that  they  occur  in  reverse  order.  This 
simplifies  the  labor  required  in  the  derivation  of  the  negative  shears; 
for,  after  computing  the  maximum  positive  shears,  these  may  be 
written  in  reverse  order,  and  the  negative  sign  prefixed;  the  result 
will  be  the  maximum  negative  shears. 

The  above  method  for  maximum  live-load  shears  is  called  the 
conventional  method.  It  is  the  one  that  is  almost  universally  used, 
and  its  use  will  be  continued  throughout  this  text. 

Exact  Method.  On  account  of  the  fact  that  the  floor  stringers 
or  joists  transfer  the  loads  to  the  panel  points,  it  would  be  impossible 
to  have  a  full  panel  live  load  at  one  panel  point  and  no  load  at  the 
panel  point  ahead  or  behind.  In  order  to  have  a  full  panel  load  at 
one  point,  the  stringers  in  the  panels,  on  both  sides  of  the  point  must 


42 


BRIDGE  ENGINEERING 


33 


be  full-loaded,  and  this  would  give  a  load  at  the  panel  point  ahead, 
provided  the  bridge  was  fully  loaded  up  to  and  not  beyond  the  panel 
point  ahead,  equal  in  value  to  one-half  of  a  full  panel  load  (see  Fig. 


Fig.  36.    Illustrating  "Exact"  Method  of  Calculating  Live-Load  Shears  in  Panels. 

36).     The  uniform  live  load,  in  order  to  produce  full  panel  loads  at 
L2,  L3  and  L4,  will  also  produce  one-half  a  panel  load  at  Lr 

By  the  methods  of  differential  calculus,  it  can  be  proved  that 
the  true  maximum  positive  live-load  shear  occurs  in  a  panel  when  the 


f 


Y//////&7//////// ///////////////////, 


-rn.  panels 


Fig.  37.    Calculating  Maximum  Positive  Live-Load  Shear  in  Panel. 

live  load  extends  from  the  panel  point  to  the  right  into  that  panel 
an  amount  (see  Fig.  37)  equal  to 


m-1    ' 
in  which, 

n  =  Number  of  the  panel  point  to  the  left  of  the  panel  under  considera- 
tion, counting  from  the  right; 
m  =  Total  number  of  panels  in  the  bridge; 
p  =  Panel  length. 

Let  the  truss  of  Fig.  35  be  considered,  the  live  load  being  2  000 


43 


34  BRIDGE  ENGINEERING 

pounds  per  linear  foot  of  truss,  and  let  it  be  required  to  determine  the 
true  maximum  positive  live-load  shear  in  the  5th  panel  from  the  right 
end. 

x  =  y-^-j  X  20  =  13.333  feet. 

There  will  now  be  (4  X  20  +  13.333)  X  2  000  =  186  666  pounds  on 
the  truss;  and  the  left  reaction  will  be { 186  666  X  (4  X  20+13.333) 
-r-  2}  -=-140  =  62  200  pounds.  From  this  must  be  subtracted  the 
amount  of  the  load  on  the  13.333  feet,  which  is  transferred  to  the 
point  Lr  This  is  equal  to  the  reaction  of  a  beam  of  a  span  equal  to 
the  panel  length,  loaded  for  a  distance  of  13.333  feet  from  the  right 
support  with  a  uniform  load  of  2  000  pounds  per  linear  foot.  This 

1  "^  c\'\f\ 
amounts  to  (13.333  X  2  000 X  -  ^~  )  -  20  =  8  890  pounds.     The 

true  shear  is  now: 

+  V3  =  +62  200  -  8  890  =   +53  310  pounds. 

The  +  V3,  as  computed  by  the  conventional  method,  was  -f  57  140, 
making  a  difference  of  3  730  pounds  between  the  two.  If  the  true 
shears  were  computed  and  compared  with  the  conventional  shears, 
it  would  be  found  that  the  Vl  would  be  the  same,  and  that  the 
remainder  of  the  conventional  shears  would  be  greater  than  the 
corresponding  true  shears.  The  difference  between  any  two  corre- 
sponding shears  would  increase  from  the  left  to  the  right  end;  that 
is,  the  difference  between  the  conventional  and  exact  shears  would 
be  greatest  in  the  panel  L5L6. 

To  get  the  maximum  negative  shear  in  any  panel,  load  from  the 
left  support  and  out  into  the  panel  under  consideration  an  amount 
p  —  x,  and  proceed  in  a  manner  similar  to  that  above  described. 

As  this  method  of  exact  or  true  shears  is  seldom  employed, 
problems  illustrating  its  application  will  here  be  omitted. 

35.  Position  of  Live  Load  for  Maximum  Moments.  In  order 
to  obtain  the  maximum  moment  at  any  point,  the  live  load  must  cover 
the  entire  bridge.  Let  the  beam  of  Fig.  34  be  considered,  and  let 
it  be  required  to  obtain  the  maximum  moment  at  the  section  a  —  a. 
The  reaction,  as  before  computed,  is: 


BRIDGE  ENGINEERING  35 


all  terms  of  which  are  positive.     The  moment  at  the  section  is : 

M  =  R,  X 
and  substituting  for  Rl  its  value, 


M=RlXx-wx~; 


But   y  =  I  —  x;   therefore, 

*—  - 


The  first  term  of  this  equation  represents  the  effect  of  the  load 
on  the  portion  x,  and  the  second  term  represents  the  effect  of  the 
load  on  the  portion  y.  The  value  of  M  will  always  be  positive.  The 
quantity  x  varies  betw?een  0  and  I.  When  x  =  0,  M  is  equal 
to  0.  When  x  =  I,  the  moment  is  equal  to  +  wy2x  -f-  2.  For 
all  values  of  x  between  0  and  I,  the  first  term  is  positive;  and  the 
second  term  being  positive  in  all  cases,  it  is  therefore  proved  that  for 
maximum  live-load  moments  at  any  point,  the  entire  span  should 
be  loaded,  as  loads  on  both  segments  add  positive  values  to  the 
moment  value. 

36.  Warren  Truss  under  Live  Load.  In  order  to  analyze  a 
truss  intelligently,  it  is  necessary  to  know  its  physical  structure; 
that  is,  it  must  be  known  what  character  of  stress  can  be  withstood 
by  the  different  members.  The  top  chords  of  all  trusses  are  built 
to  take  only  compression,  and  the  bottom  chords  are  built  to  take 
only  tension  ;  while  some  web  members  of  some  trusses  are  built  for 
tension  stresses,  some  for  compression  stresses,  and  some  for  both. 
The  characteristic  of  the  Warren  truss  is  that  the  web  members  are 
built  so  as  to  be  able  to  withstand  either  tension  or  compression. 

Let  it  be  required  to  determine  the  live-load  stresses  in  the 
Warren  truss  of  Fig.  32.  Let  the  live  load  per  square  foot  of  roadway, 
which  is  assumed  to  be  15  feet  wide,  be  100  pounds.  The  live  panel 
load  is  then  100  X  15  X  20  -i-  2  -  15  000  pounds,  and  the  live-load 
reaction  under  full  load  is  2£  X  15  000  =  37  500  pounds. 


45 


36  BRIDGE  ENGINEERING 

As  the  live  load  must  cover  the  entire  bridge  to  give  maximum 
moments  —  and  therefore  maximum  chord  stresses,  as  the  -chord  stress 
is  equal  to  the  moment  divided  by  the  height  of  the  truss  —  a  simple 
method  for  the  determination  of  live-load  chord  stresses  presents 
itself.  The  live  load  and  the  dead  load  being  applied  at  the  same 
points,  and  being  different  in  intensity,  the  stresses  produced  will 
be  proportional  to  the  panel  loads.  The  maximum  live-load  chord 
stresses  (see  Fig.  33)  will  then  be  equal  to  the  dead-load  chord  stresses 
multiplied  by  15  000  -=-  6  333  =  2.371,  and  they  are  as  follows: 

L0U1  =  -2.371  X  17700  =  -42000 
U1U2  =  -2.371  X  15833  -  -37530 
U2U3  =  -  2.371  X  25  333  =  -60  050 
U3U4  =  -2.371  X  28  500  =  -67  600 
L0L,  =  +2.371  X  7  917  =+18  770 
L,L2  =  +2.371  X  20583  =  +48800 
L2L3  =  +2.371  X  26917  =  +63850 

The  next  step  in  order  is  to  determine  the  maximum  positive 
shears,  and  from  these  write  the  maximum  negative  shears.  This 
is  done  as  follows: 

+  Live-Load  V  —  Live-Load  V 


+  2  +  3  +  4+  5)  =   +37  500  0 


6 

V2  =  ^-^(1  +  2  +  3  +  4)  =+25000  -2500 

y        16000  (1  +  2  +  3)  =  +15000  -7500 

6 

V4  =  1500°  (1  +  2)  =   +    7  500  -  15  000 

+   2  500  -  25  000 

+  0  -37500 

The  stresses  produced  by  the  positive  shears  are  called   the 
maximum  live-load  stresses,  and  are: 

+  L0U,  cos  (£  +  37  500  =  0  .-.  L0Ul  =  -37  500  X  1.12  =   -42  000 

-  U,L,  cos  <j>  +  37  500  =  0  .-.  l^L,  =  +37  500  X  1  12  =   +42  000 
+  L1U2  cos  0  +  25  000  =  0  .'.  L,C72  =  -25  000  X  1.12  =  -28  000 

-  C72L2  cos  <f>  +  25  000  =  0  /.  C72L2  =  +25  000  X  1.12  =   +28  000 
+  L2C73cos<£  +  15000  =  0  .-.  L2C73  =  -15000  X  1.12  =   -16800 

-  U3L3  cos  0  +  15  000  =  0  .'.  U3L3  =  + 15  000  X  1.12  =  +16  800 

The  stresses  produced  by  the  negative  shears  are  called  the 
minimum  live-load  stresses,  and  are: 


46 


BRIDGE  ENGINEERING 


37 


+  LJJl  cos  0  +  0         =0 

-  f7,L,  cos  <}>  +  0         =0 
+  L1?72cos  $  -  2500  =  0 

-  U2L2  cos  0  -  2  500  =  0 
+  L2U3cos  <j)  -  7500  =  0 

-  U3L3  cos  0  -  7  500  =  0 


.-.  £,„£/,  =  0 

.-.  E7.L,  =  0 

.-.  L,U2  =   +2500  X  1.12  =  +2800 

.-.  U^  =   -2  500  X  1.12  =  -2  800 

.-.  L2[/3  =   +7  500  X  1.12  =  +8  400 

.-.  U3L3  =  -  7  500  X  1.12  =  -8  400 


These  stresses,  together  with  the  dead-load  stresses,  should 
now  be  placed  together  as  a  half-diagram,  as  is  done  in  Fig.  38,  the 
stresses  being  rounded  off  to  the  nearest  ten  pounds  and  then  ex- 
pressed in  thousands  of  pounds.  No  minimum  live-load  stress  is 
given  for  the  chords,  as  this  will  evidently  be  zero  in  all  cases,  since 
no  position  of  the  live  load  will  cause  a  reversal  of  stress.  It  will  be 
seen  that  the  stresses  produced  by  the  negative  shears  are  of  opposite 


Fig,  38.    Dimension  and  Stress  Diagram  of  Warren  Half-Truss  under  Live  Load. 

sign  from  the  stress  produced  by  the  dead  load,  and  these  tend  to 
decrease  the  dead-load  stress  by  that  amount;  and  in  some  cases 
(see  LI  U3  and  U3  L3,  Fig.  38)  it  will  be  so  large  as  to  overcome  the 
dead-load  stress  and  therefore  change  the  total  stress  from  one  kind 
to  another.  Do  not  forget,  in  considering  any  combination  of  the 
above  stresses,  that  the  dead  load  occurs  with  either  the  maximum 
or  the  minimum  live  load,  but  not  with  both  at  the  same  time. 

37.  Counters.  By  reference  to  ?73  Ls  (Fig.  38),  it  is  seen  that 
when  the  live  load  is  on  the  panel  points  Lt  and  L2  the  total  stress  in 
the  member  is  +  3.54  +  (—  8.40)  =  —4.86,  a  compressive  stress  of 
4  860  pounds;  whereas,  under  dead  load  alone,  the  stress  was  +  3.54, 
a  tensile  stress  of  3  540  pounds.  If  the  member  U3  L3  had  been  built 
of  long,  thin  bars  which  could  take  only  tension,  and  which  con- 
sequently would  have  doubled  up  under  the  resultant  compression 


47 


38 


BRIDGE  ENGINEERING 


brought  upon  them  by  the  combined 
action  of  the  dead  and  minimum  live- 
load  stresses,  then  this  member  could 
not  be  used  in  this  case,  but  some 
other  arrangement  would  be  necessary 
in  order  to  insure  the  stability  of  the 
truss. 

In  the  Warren  truss,  no  special  ar- 
rangement is  necessary,  as  the  web 
members  are  built  so  as  to  take  either 
tension  or  compression;  but  with  the 
Pratt  and  Howe  trusses  some  special 
arrangement  is  necessary,  as  the  diag- 
onals are  built  to  take  one  kind  of 
stress  only.  The  case  of  the  Pratt  will 
be  considered  first. 

The  Pratt  truss  has  the  diagonals 
made  of  long  bars  which  take  tension 
only,  and  the  intermediate  posts  are 
constructed  so  as  to  be  able  to  take 
compression  only.  It  is  not  necessary 
to  consider  the  intermediate  posts,  for 
the  action  of  the  web  members  is  such 
that  the  resulting  stresses  are  always 
compressive. 

Let  the  13-panel  Pratt  truss  of 
Fig.  39  be  considered.  The  panel 
length  is  18  feet,  the  height  25  feet,  the 
dead  panel  load  22  000  pounds,  and 
the  live  panel  load  58  500  pounds. 
The  secant  is  (182  +  252  )*  -=-  25  = 
1.231.  The  dead-load  shears  and  the 
maximum  and  minimum  live-load 
shears  are  placed  directly  below  their 
respective  panels.  Only  those  mem- 
bers are  shown  full-lined  in  Fig.  39 
which  act  under  the  dead  load.  Note 
that  the  dead -load  shears  in  the  center 


48 


BRIDGE  ENGINEERING  39 

panel  being  zero/the  dead-load  stress  in  the  diagonals  in  the  center 
panel  would  be  0  X  sec  </>  =  0. 

In  the  first  four  panels  from  either  end,  the  live-load  shear, 
which  is  of  a  different  sign  from  that  of  the  dead-load  shear,  is 
smaller  than  the  dead-load  shear,  and  therefore  will  not  cause  a 
reversal  of  stress  in  the  member  in  that  panel.  For  example,  take 
U3Lt;  then,  for  dead-load  stress, 

-C73L4  cos  <£  +  66.0  =  0  --.U3L3  =  +66.0  X  1.231  =   +81.20 

For  live-load  stress, 

-C/3L4  cos  <£  -  27.0  =  0  .-.U3L3  =   -27.0  X  1.231  =   -33.25 

The    total    stress  =  +  81.20  -  33.25  =  +  47.95,    which    is    still 
tension. 

Considering  L9  U10,  the  stress  equations  are : 
For  dead-load  stress, 

+  L9f/10  cos  <£  -  66.0  =  0  /.  L0U}0  =   +81.20 

For  live-load  stress, 

+  L9t/10cos  <£  +  27.0  =  0  .:L0UM  =   -33.25 

The  total  stress,  as  before,  is  +  47.95,  or  a  tension  of  47  950  pounds. 

An  inspection  of  the  center  panel  and  the  two  panels  on  each 
side  of  it,  shows  that  the  live-load  shear  is  of  a  different  sign  from 
the  dead-load  shear,  and  is  also  greater  in  value  than  the  dead-load 
shear.  If  the  members  shown  in  Fig.  39  were  the  only  ones  in  the 
panels,  then  the  dead-load  stresses  would  be: 

-  U4L5  cos  0  +  44.0  =  0  £/4L5  =   +  54.20 
-t/5L6cos  0  +  22.0  =  0  t/5L6  =   +27.10 
+  L7UKcos  <f>  -  22.0  =  0  L7US  =  +27.10 
+  LJT0  cos  <£  -  44.0  =  0  LKU9  =  +54.20 

and  the  live-load  stresses  caused  by  the  shear  of  opposite  sign  from 
that  of  the  dead-load  shear,  are: 

-t/4L5cos  $  -  45.0  =  0  t/4Ls  =   -55.40 

-  USL0  cos  $  -  67.5  =  0  f/5L6  =   -83.10 
+  L7C78cos  i  +  67.5  =  0             L7f/8  =   -83.10 
+  LaU9  cos  0  +  45.0  =  0             L8C7fl  =  -55.40 

As  no  diagonal  acts  under  dead  load  in  the  center  panel,  we  may 
assume  that  C/6  L1  acts  under  live  load.  The  stresses  which  occur 

in  this  are: 

+  UtiL7  cos  $  +  94.5  =  0  UKL7  =   +116.30 

-  UbL7  cos  <j>  -  94.5  =  0  UeL7  =   -  116.30 


40  BRIDGE  ENGINEERING 

The  above  shows  that  compressive  stresses  will  occur  in  the 
diagonals  which  were  built  for  tension  only.  These  stresses  are : 

C74L5  =   +54.20  -     55.40  =  -      1  200  pounds 

C76L6  =  +27.10  -     83.10=  -56000      " 

L7U8  =  +27.10-    83.10=  -   56000      " 

LSU9  =  +54.20  -     55.40  =  -      1  200      " 

U6Lj  =  0  -  116.30  =  -116  300      " 

If  some  provision  were  not  made  for  these  stresses,  they  would  cause 
the  members  to  crumple  up  and  the  truss  to  fail.  In  order  to  allow 
for  them,  diagonals  are  placed  in  the  panels,  as  shown  by  the  dotted 
and  dashed  lines.  These  members  will  take  up  the  above  stress; 
and  moreover,  as  they  slope  the  opposite  way  from  the  main  members, 
they  will  be  in  tension. 

In  order  to  prove  this,  assume  L5U9  to  act  when  the  live  load  is  on 
points  L5,  L4,  L3,  L2,  and  Lr     Now,  U5L6  will  not  be  regarded,  as  its 
stress  will  be  zero.     Then  the  stresses  will  be: 
For  dead  load, 

+  L5f/0  cos  <£  +  22.0  =  0  L5[/6  =   -27.10. 

For  live  load, 

+  L5£7U  cos  $  -  67.5  =  0  LJJ6  =  +83  10; 

and  the  total  stress  in  L,U6  will  be  -  27.10  +  83.10  =  +  56.00. 

In  a  similar  manner,  the  stresses  in  the  other  members  are:  LJJ5 
-  +1.2;  L6U7=+  116.30;  U,LS  =+  56.00;  and  £78L9=+1.2. 
These  diagonals  are  called  counters  or  counter-bracing. 

From  a  consideration  of  the  foregoing,  it  is  evident  that: 

(a)  //  the  live-load  shear  in  any  panel  is  of  opposite  sign  and  greater 
than  the  dead-load  shear  in  the  same  panel,  then  a  counter  is  required. 

(b)  The  stress  in  a  counter  is  equal  to  the  algebraic  sum  of  the  dead-load 
shear  and  the  live-load  shear  of  opposite  sign  times  the  secant  of  the  angle  it 
makes  with  the  vertical. 

This  is  true  for  any  truss  with  horizontal  chords  and  a  simple  system 
of  webbing  with  diagonals  and  verticals. 

38.  Maximum  and  Minimum  Stresses.  Some  specifications 
require  the  member  to  be  designed  for  the  maximum  stress,  while 
others  take  into  account  the  range  of  stress.  In  this  latter  case  it 
is  necessary  to  determine  the  minimum  as  well  as  the  maximum  stress. 
Except  where  a  reversal  of  stress  occurs — and  this  does  not  happen 
in  trusses  with  horizontal  chords — few  specifications  require  any 


50 


BRIDGE  ENGINEERING 


11 


but  the  maximum  stresses  to  be  com- 
puted. For  that  reason,  little  space 
will  here  be  devoted  to  the  minimum 
stresses,  their  computation  in  succeed- 
ing articles  being  thought  to  illustrate 
them  sufficiently. 

(a)  The  maximum  stress  in  a  member 
is  equal  to  the  sum  of   the   dead-load  stress 
and  the  live-load  stress  of  the  same  sign. 

(b)  The  minimum  stress   is  equal   to 
the  sum  of  the  dead-load  stress  and  the  live- 
load  stress  of  the  opposite  sign,  or  to  the  dead- 
load  stress  alone,  according  to  which  gives 
the  smallest  value  algebraically.     By  this 
latter  statement  it  should  be  seen  that  if 
the  maximum  stress  is  —58.60,  then  0  or 
+  18.00  would  be  smaller  than  -3.00. 

(c)  It  is  evident  that  the  minimum 
in   all    counters    and  in  all  main  members 
in  panels  where  counters  are  employed  will 
be  zero,  for  when  the  counter  is  acting  the 
main  member  is  not,  and  therefore  its  stress 
is  zero.    The  reverse  is  also  true. 

(d)  An  exception  to  a  is  seen  in  the 
case  of   the  counters.     Here  it  is  evident 
that  the  maximum  stress  is  equal  to  the 
algebraic  sum  of  the  dead-load  shear  and 
the  live-load  shear  of  opposite  sign  times 
the  secant  of  the  angle  which  the  counter 
makes  with  the  vertical. 

While  it  is  true  that  in  trusses  with 
horizontal  chords  the  loading  for  maxi- 
mum shears  will  give  the  maximum 
live-load  stress  to  be  added  to  the 
dead  load  for  the  maximum  stress,  it  is 
not  always  true  that  the  loading  for 
minimum  live-load  shears  will  give  the 
stress  to  add  to  the  dead-load  stress  to 
get  the  minimum  stress.  However,  the 
loading  for  the  minimum  live-load 
shears  will  give  the  live-load  stress  to 
be  added  to  the  dead-load  stress  for 
the  minimum  stress,  except  in  the  case 


51 


-12 


BRIDGE  ENGINEERING 


U 


of  verticals  placed  between  panels  each  of  which  contains  counters, 
and  in  that  case  it  may  or  may  not  do  so.  In  such  cases  a  loading 
must  be  assumed — preferably  the  one  for  minimum  shears — and 
the  shears  in  the  panels  on  each  side  of  the  vertical  must  be  com- 
puted for  the  loading  assumed. 
If  the  resultant  shear  is  the  same 
sign  as  the  live  load,  then  the 
main  diagonal  acts;  if  it  is  of 
different  sign,  then  the  counter 
acts. 

As  an  example,  let  it  be  re- 
quired to  find  the  minimum  stress 
in  the  vertical  U5L5  of  the  truss 
of  Figs.  39  and  40.  It  is  assumed 
that  the  loading  for  minimum 
shears  will  give  the  result.  The 
section  a  —  a  is  then  passed,  and 
the  live  load  placed  on  L.  and  all 
points  to  the  left.  The  shears  will 
then  be  as  shown  in  Fig.  41.  To 
obtain  the  shear  in  the  panel  LtL5, 


aiv. 

4-  44.0 

.+    22.0 

llv. 

9.0 

-     67.5 

Totalv 

4- 

— 

Fig.  41.    Stress  Diagram  for  Vertical  iii 
Truss  of  Fig.  40. 


under  this  loading,  it  must  be  re- 
membered that  a  load  is  at  L5;  and  so  the  shear  is  the  shear  in  the 
panel  I/5L6  with  the  panel  load  at  I/5  added,  or,  —67.5  +  58.5  = 
—  9.0.  The  diagonals  now  act  as  indicated  by  Fig.  41,  and  the  total 
stress  in  C75L5  is  determined  by  passing  a  circular  section  around  LT5, 
and  it  is  : 

-Load  at  f/5-  f/5L5  =  0. 

As  there  is  no  load  at  U5,  the  stress  in  C75L5  is  =  0.  The  same  result 
will  occur  if  points  L4  or  L3  and  to  the  left  are  loaded;  but  if  points 
L2  and  to  the  left  are  loaded,  the  members  C74L5  and  ?75L6  will  act, 
and  the  stress  in  U5L5  will  then  be  equal  to  the  shear  on  the  section 
a  —  a.  The  stresses  are:  Dead-load,  —  22.0;  and  live-load,  + 
13.5,  which  gives  a  total  of  —  8.5;  but  as  the  maximum  stress  is 
-22.0  -  126.0  =  -  148.0,  it  is  evident  that  0  and  not  -8.5  is  the 
minimum. 

The  computation  of  the  maximum  stress  is  as  follows: 

Load  points  L6  and  to  the  right.     The  shear  on  a  —  a  is,  for 


BRIDGE  ENGINEERING 


43 


dead  load,  +22.0;  and  for  +  live  load,  +126.0;  and  the  equations  of 
the  stresses  are: 

+   22.0  +  C/5L5  =  0          C75L5  =   -   22.0 

+  126.0  +  U5L5  =  0         C75LS  =   -  126.0 

Max.  =   -  148  0 

TRUSSES   UNDER   DEAD  AND  LIVE   LOADS 

39.  The  Pratt  Truss.  The  Pratt  truss  is  used  to  perhaps  a 
greater  extent  than  any  other  form;  probably  90  per  cent  of  all  simple 
truss  spans  are  of  this  kind. 

Let  it  be  desired  to  determine  the  stresses  in  the  8-panel  200-foot 
single-track  span  shown  in  Fig.  42,  the  height  being  30  feet,  the  dead 
panel  load  being  30  000  pounds,  and  the  live  panel  load  62  400 

pounds.    The  secant  is  {^  +~3()2)  *  +  30  =  1-302,  and  the  cosine 

is  0.7685.     The  dead-load  reaction  is  3£  X  30.0  =  105.0. 
The  dead-load  shears  are : 

y,  =  +105.0 
V,  =  +  75.0 
V3  =  +  45.0 
V4  =  +  15.0 
F5  =  -  15.0 

The  dead-load  chord  stresses  may  be  tabulated  as  follows  (see 
Articles  27  and  29): 

Dead- Load  Chord  Stresses 


MEMBER 

SEC- 
TION 

CEN- 
TER OF 
MO- 
MENTS 

STRESS  EQUATION 

STRESS 

L0L,  =  L,L2 

a  —  a 

ul 

+  105.0  X  25  -  L,L2  X  30  =  0 

+    87.5 

T    T 

^2-^3 

b-b 

U2 

+  105.0  X  50  -  30.0  X  25  -  L2L3  X 

30  =  0 

+  150.0 

L3L4 

c  —  c 

U3 

+  105.0  X  75  -  30.0  (25  +  50)  -  L3L4 

X  30  =  0 

+  187.5 

UJJ* 

a  —  a 

L2 

+  105.0  X  75  -  30.0  X  25  +  U,U2  X 

30  =  0 

-150.0 

uau, 

b-b 

L3 

+  105.0  X     75  -  30.0  (25  +  50)  + 

U2U3  X  30  =  0 

-187.5 

U3U, 

c  —  c 

L< 

+  105.6  X  100  -  30.0  (25  +  50  +  75) 

+  U3U4  X  30  =  0 

-200.0 

In  determining  dead-load  stresses  in  web  members,  it  is  cus- 
tomary to  assume  one-third  of  the  dead  panel  loads  as  applied  at  the 


II 


BRIDGE  ENGINEERING 


upper  chord  points.  This,  as  will  be  seen,  makes  no  difference  in  the 
stresses  in  the  chords  or  in  the  diagonals,  the  stresses  in  the  verticals 
only  being  different  from  what  is  the  case  when  all  the  dead  load  is 
taken  on  the  lower  chord. 

The  stresses  in  the  diagonals  (see  Articles  27,28,  and  30)  are: 

Dead-Load  Stresses  in  Diagonals 


MEM- 
BER 

SEC- 
TION 

SHEAR   ON 
SECTION 

ST 

RESS 

EQUATION 

STRESS 

LU, 

0  —  0 

+  105.0 

+  105.0  + 

LnU 

,  X  0.7685 

=  0 

-136.70 

UiL2 

a  —  a 

+    75.0 

+    75.0  - 

t/jZ/ 

2  X  0.7685 

=  0 

+    97.60 

U  L 

b-b 

+   45.0 

+    45.0  - 

U  L 

3  X  0.7685 

=  0 

+    58.60 

U3L4 

c  —  c 

+    15.0 

+    15.0  - 

U3L 

4  X  0.7685 

=  0 

+    19.53 

In   determining  the  stresses  in  the  verticals,  it  is  to  be  remem- 
bered that  one-third  the  dead  panel  load  (or  10.0)  is  at  the  panel 


o  a  'i  b        -     2  c 

Fig.  42.    Outline  Diagram  of  8-Panel  Single-Track  Pratt  Truss  Span. 

points  of  the  upper  chord,  and  two-thirds  (or  20.0)  is  at  the  lower 
chord.  The  stress  in  the  hip  vertical  UlLl  is  determined  by  passing 
a  circular  section  around  L,.  It  is  solved  thus: 

-20.0  +  f/.L,  =  0         t/A  =   +20.0 
In  a  similar  manner  the  stress  in  U4L4  is  found  to  be : 

-10  -  U4L4'=  0        U4L4  =  -10.0 

In  order  to  find  the  stress  in  the  remaining  verticals,  sections  1  —  1 
and  2  —  2  are  passed,  cutting  them,  and  the  shears  on  these  sections 
computed.  The  shears  are: 

F,_,  =   +  105.0  -  2  X  20  -  1  X  10  =   +55.0 
F2-2  =   +  105.0  -3X20-2X10=   +25.0 

The  stress  equations  are  written,  remembering  that  as  the  verticals 


54 


BRIDGE  ENGINEERING 


45 


make  an  angle  of  zero  with  the  vertical,  their  cosine  is  equal  to  unity. 

These  equations  are: 

+  U2L2  +  55.0  =  0  U2L2  =   -55.0 

+  U3L3  +  25.0  =  0  U3L3  =   -25.0 

The  live-load  chord  stresses  will  be  proportional  to  the  dead- 
load  chord  stresses,  as  both  loads  cover  the  entire  truss  in  exactly 
the  same  manner.  The  ratio  of  the  panel  loads  by  which  the  dead- 
load  chord  stresses  are  multiplied  in  order  to  get  the  live-load  chord 
62  400 


stresses,  is 


=  2.08,  and  the  chord  stresses  are: 


Ul 


\ 


30000 

LUL,  =  L,L2  =  +  87.5  X  2.08  =  + 182.0 
L2L3  =  +150.0  X  2.08  =  +312.0 
L3L4  =  +187.5  X  2.08  =  +390.0 
U1U2  =  -150.0  X  2.08  =  312.0 
U2U3  =  -1875  X  2.08  =  -390.0 
U3U4  =  -200.0  X  2.08  =  -416.0 

As  the  entire  bridge  is  to  be  loaded  to  get  the  maximum  stress  in 
I/oC/j,  it  is  therefore  equal  to  the 
dead-load   stress   times  the  above 
ratio;  or  L0Ut  =  -136.70  X  2.08 
-  284.20. 

The  maximum  live-load  stress 
in  U1L1  is  determined  by  passing 
a  circular  section  around  Lv  and 
is  solved  (see  Fig.  43)  from  the 
equation : 

+  U,L  -  62.4  =  0  .'.  17, L!  =  +62.4 
For  VJjv  the  section  a  —  a  is 
passed,  and  the  points  L2  and  to 
the  right  are  loaded.  The  maxi- 
mum  shear  is: 

+  V2  =   +  -^p  (1+2  +  3  +  4  +  5  +  6)=   +  163.8; 

and  the  stress  equation  is: 

+  163.8  -  U,L2  X  0.7685  =  0  .'.  U,L2  =   +213.2. 

In  a  similar  manner,  pass  section  b  —  b,  and  load  points  L3  and  to 
the  right,  and  the  shear  and  the  stress  equations  for  U2L3  are : 

+  V3  =   +  -^i  (1+2  +  3  +  4  +  5)=   +117.0 
+  117.0  -  U2L3  X  0.7685  =  0  .'.  U2L3  =   +152.4 


55 


46 


BRIDGE  ENGINEERING 


For  UJji,  the  section  c  —  c  is  passed,  and  the  panel  points  to  the 
right  are  loaded.  The  shear  and  stress  equations  are: 

+  V4  =   +  -6|^  (1  +  2  +  3  +  4)  =   +78.0 

O 

+  78.0  -  C73L4  X  0.7685  =  0  .'.  U3L4  =   +101.6 

For  the  maximum  stresses  in  the  verticals,  sections  1  —  1,  2  —  2, 
and  3  —  3  are  passed,  and  in  each  case  the  panel  points  to  the  left 
of  these  loaded.  The  shears  are 

Fj  _ ,  =  -^  (1+2  +  3  +  4  +  5)=  +117.0 

O 

62.4 


V,-,  =  -  ~-    (1  +  2  +  3  +  4)  =   +78.0 
+  2  +  3)  =   +46.8 


AO  4 

F8_,  =       £- 


U 


+  117.0  +  f/2L2  =  0 
+    78.0  +   C73L3  =  0 


u, 


\ 


The  stress  equations  for  U2L2  and  U3L3  are  simple,  as  only  three 
members  are  cut.     They  are: 

.-.  f/2Lo=  -  117.0 
.-.  U3L3  =  -     78.0 

It  is  seen  that  the  section  3  —  3  cuts  the  member  LJ75,  and 
therefore  the  stress  in  this  must 
be  determined  before  the  stress 
equation  can  be  written,  as  its  ver- 
tical component  will  enter  into  it. 
However,  by  comparing  the  dead- 
load  shear  in  that  panel,  which  is 
—  15.0,  and  the  live-load  shear  F3_3, 
which  is  +46.8,  it  is  seen  that  the 
resultant  shear  is  +  ;  and,  as  this 
is  of  opposite  sign  from  the  dead- 
load  shear,  a  counter  is  required 
and  is  acting.  The  stress  in  U5L4  is  zero,  and  the  diagonals  act  as 
in  Fig,  44,  the  section  3  —  3  then  cutting  three  members.  The 
stress  equation  is  +  46.8  +  UtL4  =  0,  from  which  U4L4  =  -  46.8. 
Care  should  be  taken  not  to  add  to  this  -46.8  the  -10.0 
derived  as  dead-load  stress  on  page  44,  in  order  to  get  the  maximum 
stress,  as  the  —10.0  previously  derived  was  the  dead-load  stress 
in  UJj4  when  U3L4  and  LJJb  were  acting.  The  dead-load  stress  which 
goes  with  the  live-load  stress  of  —46.8  acts  simultaneously  with  it, 


\   \- 


Fig.  44.    Calculation  of  Stress  in  Diag 
onal  of  Span  of  Fig.  42. 


56 


BRIDGE  ENGINEERING  47 

and  is  the  dead-load  stress  in  U^L^  when  the  members  U,L4  and  U4L5 
are  acting  as  in  Fig.  44.  The  dead-load  shear  on  the  section  3  —  3 
would  then  be  the  left  reaction  minus  the  loads  at  points  Uv  U2,  U3, 
Lv  L2,  L3and  L4;  or, 

F3_3  =   +105.0  -3X10-4X20=  -5.0; 
and 

-5.0  +  U4Lt  =  0  .-.U4Lt  =  +5.0. 

Remember  that  this  +5.0  can  act  only  when  the  live  load  tends  to 
produce  a  stress  of  —46.8;  and  thus  the  total  stress  in  C74L4  with  live 
load  in  that  position  is  -46.8  -f  5.0  =  -43.8,  while  with  dead  load 
only  in  the  truss  the  stress  is  — 10.0. 

The  dead-load  shears  and  the  maximum  +  and  —  live-load 
shears  should  now  be  written  for  inspection,  in  order  to  investigate 
for  counters  and  then  for  the  minimum  stresses.  Those  whose 
derivation  has  not  been  given  should  be  easily  computed  by  the  stu- 
dent at  this  time.  The  shears  are 


DEAD-  LOAD 

+  LlVE-LOAD 

—  LlVE-LOAD 

Vl            +  105.0 

+  218.4 

0 

F2         +    75.0 

+  163.8 

-   7.8 

V3         +   45.0 

+  117.0 

-23.4 

V4         +   15.0 

+    78.0 

-46.8 

From  a  study  of  these  it  is  seen  that  a  counter  is  required  in  the 
4th  panel  according  to  rule  a,  Article  37;  and  according  to  rule  b  of 
the  same  article,  the  maximum  stress  is  (-46.8  -f  15.0)  X  1.302  = 
+  41.4,  the  minimum  stress  for  it  and  also  U,Lt  being  zero  according 
to  the  same  article.  A  counter  is  also  required  in  panel  5,  as  the 
truss  is  symmetrical. 

The  minimum  live-load  stress  in  U^  is  zero,  and  occurs  when 
no  live  load  is  at  the  point  Lr 

The  minimum  live-load  stresses  in  the  diagonals  U^  and  ?72L3 
occur  when  the  truss  is  loaded  successively  to  the  left  of  the  sections 
a  —  a  and  b  —  b,  in  which  case  the  shears  are  —7.8  and  —23.4 
respectively.  The  stress  equations  are 

-U,L2-     7.8X0.7685  =  0  .-.  UtL2  =-  10.16 

-U2L3  -  23.4  X  0.7685  =  0  .'.  U2L3  =  -29.15 

The  minimum  live-load  stress  in  U^  is  obtained  by  passing 


57 


48 


BRIDGE  ENGINEERING 


section  1  —  1  and  loading  the  panel  points  to  the  left.  The  live-load 
shear  is  the  same  at  this  section  as  it  is  at  the  section  6  —  6  — namely, 
—  23.4.  The  stress  equation  is 

+  U2L2  -  23.4  =  0  .'.  U2L2  =   +23.4 

To  determine  the  minimum  live-load  stress  in  U3L3,  proceed  as 
indicated  on  page  42.  By  loading  points  L3  and  to  the  left,  the  live- 
load  shear  in  the  4th  panel  will  be  —46.8,  and  in  the  3d  panel  under 
this  same  loading  it  will  be  -46.8  +  62.4  =  + 15.6.  The  sign  of  the 
total  shear  in  the  two  adjacent  panels,  and  the  members  acting,  are 
shown  in  Fig.  45.  The  stress  in  U3L3  is  then  determined  by  using  a 


10 


10 


10 


eo.o 

©E4 


10 
U5 


L4- 

eo.o 


Ls 
eo.o 


d.lv. 

+  4-5.O 

+  I5.O 

l.l.v. 

•*•     1  5.6 

—  4-6.6 

Totalv 

+ 

— 

d.l.v. 

+  15.0 

-  15.0 

l.l.v. 

-  15.6 

-78.0 

Total  v 

— 

— 

Fig.  45. 


Fig.  46. 


Stress  Diagrams  for  Verticals  hi  Span  of  Fig.  42. 

circular  section  around  U3,  and  is  simply  the  dead  load  at  U3,  there 
being  no  live-load  stress  in  the  member  when  the  bridge  is  loaded  as 
has  been  done. 

In  finding  the  minimum  live-load  stress  and  also  the  minimum 
stress  in  UtLv  the  same  method  of  procedure  will  be  followed.  Let 
L^  and  to  the  left  be  loaded.  Then  the  shear  in  the  5th  panel  is 
—  78.0,  and  under  this  same  loading  the  shear  in  the  4th  panel  is 
-78.0  +  62.4  -  -15.6.  The  sign  of  the  total  shear  in  each  of  the 
adjacent  panels  is  given  in  Fig.  46.  It  should  be  remembered  that 
a  resultant  shear  with  the  same  sign  as  the  dead-load  shear  causes 
the  main  diagonal  to  act,  while  a  resultant  shear  of  opposite  sign  to 
that  of  the  dead-load  shear  causes  the  counter  to  act.  The  members 


58 


BRIDGE  ENGINEERING 


49 


acting  are  shown,  and  a  section  4  —  4  can  be  passed.  The  dead-load 
shear  at  this  section  is  105  -  3  X  20  -  4  X  10  -  +5.0;  and 
accordingly, 

-  U4L4  +  5.0  =  0. 
Therefore, 

U4L4  =  +  5.0  =  Dead-load  stress  in  this  case. 
The  live-load  stress  which  acts  at  the  same  time  is: 

-U4L4  -  15.6  =  0  .-.  U4L4  =   -15.6, 

the  term  — 15.6  representing  the  live-load  shear  on  the  section  4  —  4. 
This  is  not  the  minimum  stress,  as  will  next  be  shown,  but  it  illus- 
trates the  fact  that  the  loading  for  minimum  live-load  shears  does 
not  always  give  the  minimum 
live-load  stress. 

By  loading  Lv  the  live-load 
shear  in  the  second  panel,  and 
likewise  all  others  from  this  to 
the  right  support,  will  be  —7.8. 
The  total  shears,  together  with 
their  sign,  and  also  the  members 
they  cause  to  act,  are  given  in 
Fig.  47.  The  minimum  live-load 
stress  in  U4L^  is  found  to  be  zero, 
and  the  dead-load  stress  is  —  10, 
as  is  derived  by  passing  a  circular 
section  around  U 4,  the  equation 


10 


°U4 


10 


eo 


I 


EO 


Ls 
eo 


d.l.v. 

+  15.0 

-15.0 

U.v 

-   7.8 

-    7.8 

Total  v 

+ 

— 

Fig.  47.    Stress  Diagram  for  Vertical  in 
Span  of  Fig.  42. 


being  as  follows: 

-Live  load  at  Ut  -  U4Lt  =  0         .'.  U4L4  =  0  for  live  load. 
-Dead  load  at  U4-  U4L4  =  0         .'.  U4L4  =  - 10.0  for  dead  load. 

A  diagram  of  half  the  truss  should  now  be  made,  and  all  dead 
and  live  load  stresses  placed  upon  it,  and  these  should  be  combined  so 
as  to  form  the  maximum  and  the  minimum  stresses.  Such  a  dia- 
gram, together  with  all  stresses,  is  given  in  Fig.  48. 

The  stresses  are  written  in  the  following  order:  Dead  load, 
maximum  live  load,  minimum  live  load,  the  maximum,  and  the 
minimum.  In  the  chord  and  end-post  stresses,  there  is  no  minimum 
live-load  stress  recorded,  it  being  zero.  Where  pairs  of  stresses  occur 
simultaneously,  a  bent  arrow  connects  them. 

40.    The  Howe  Truss.    The  physical  make-up  of  the  Howe  truss 


59 


50 


BRIDGE  ENGINEERING 


QpOO 

o  —  ^ 

II  1 1 


!   I  I 


o0O.Q 


n-XO1000 
'QirrU 

•H-  +  + 


differs  from  that  of 
the  Pratt  in  that 
the  diagonals  are 
made  to  stand  com- 
pression only,  and 
the  verticals  can 
stand  tension  only. 
In  the  Pratt  truss 
it  was  found  that 

M 

g  none  of  the  inter- 

.2  mediate  posts  could 

5]  be     brought     into 

I  tension     by     any 

^  loading.      In      the 

£  Howe  truss  it  will 

3  be  found  that  none 

E  of  the  verticals  can 

a     be     brought     into 

. 
OQ     compression. 

^  Let  it  be  required 
to    determine    the 

|  stresses  in  a  Howe 

3  truss   of  the   same 

g  span,    height,    and 

K  loading  as  the  Pratt 

"  truss  of  Article  39. 

tc 

E  An  outline  diagram 
is  given  in  Fig.  49. 
The  dead-load 
shears  and  the 
maximum  and  min- 
imum live-load 
shears  will  be  the 
same  as  for  the 
Pratt  truss,  and 
they  are : . 


BRIDGE  ENGINEERING 


51 


DEAD-LOAD  V 

+  LIVE-LOAD  V 

-  LIVE-LOAD  V 

V        +  105.0 

+  218.4 

-    0 

r     +  75.0 

+  163.8 

-    7.8 

V       +   45.0 

+  117.0 

-23.4 

V       +    15.0 

+    78.0 

-46.8 

V       -    15.0 

+    46.8 

-78.0 

Inspection  of  these  shows  that  counters  are  required  in  the  4th 
and  5th  panels  (see  Article  37). 

The  dead-load  lower  chord  stresses  will  be  computed  by  the 


U,    /          UE  /         U3    /  :       U4     / 


Pig.  49.    Outline  Diagram  of  8-Panel  Single-Track  Howe  Truss  Span. 

tangent  method  (see  Article  31),  the  section  being  y  —  y{,  etc.  The 
tangent  of  <£  is  25  -=-  30  =  0.8333.  The  stresses  may  be  conven- 
iently tabulated  as  follows: 

Dead-Load  Chord   Stresses  (Lower  Chord) 


MEM- 
BER 

SECTION 

STRESS  EQUATION 

STRESS 

LnL, 

y  -  Vi 

-  105.0  X  0.8333  +  L0L,  =  0 

+    87.5 

LtL2 

y  —  y-i 

-(105.0  +  75.0)  0.8333  +  L,L2  =  0 

+  150.0 

L9L3 

y  —  y* 

-(105.0  +  75.0  +  45)  0.8333  +  L2La  =  0 

+  187.5 

L3L4 

y  -  2/4 

-(105.0  +  75.0  +45.0  +  15.0)  0.8333  +  L3L4  =  0 

+  200.0 

A  simple  method  for  the  determination  of  the  upper  chord 
stresses,  is  to  pass  a  section  and  to  equate  the  sum  of  the  horizontal 
forces.       Pass  section  1  —  1.     The  only  horizontal  forces  are  the 
stresses  in  I/^  and  UJ72;  and  as  these  are  parallel,  one  must  be  equal 
and  opposite  to  the  other.  In  a  like  manner  the  stresses  in  the  other 
sections  of  the  top  chord  are  found.     The  stresses  are : 
U,U2  =  -L0L,  =  -(+   87.5)  =   -  87.5 
U2U3  =   -L,L2  =   -(  +  150.0)  =   -150.0 
U3U4  =   -L2L3  =   -(  +  187.5)  -   -187.5 


61 


52  BRIDGE  ENGINEERING 

A  consideration  of  the  Pratt  truss  shows  that  this  method  can  be 
applied  to  it  in  determining  the  chord  stresses. 

As  it  is  known  that  the  diagonal  web  members  are  in  compression 
under  the  dead  load  which  produces  a  positive  shear  in  the  left  half 
of  the  truss,  it  is  evident  that  positive  live-load  shears  will  produce 
compressive  stresses,  and  negative  live-load  shears  tensile  stresses, 
in  the  diagonals  in  the  left  half  of  the  truss.  Also,  from  Article  30, 
the  stress  in  a  diagonal  is  V  sec  <£.  The  stresses  can  now  be  written 
directly  without  the  aid  of  the  stress  equation : 

L0Ul  =  -105.0  X  1.302  =  -136.70 

L,£72  =  -    75.0  X  1.302  =  -   97.60 

L,U3  =  -   45.0  X  1.302  =  -   58.60 

L~[74  =  -    15.0  X  1.302  =  -    19.53 

Likewise  the  stresses  in  the  verticals  can  be  written  directly,  remem- 
bering that  here  the  secant  is  unity,  and  that  the  shear  at  the  section 
cutting  the  member  is  to  be  used,  not  forgetting  that  J  of  the  dead 
panel  load  is  applied  at  the  top  panel  points.  The  shears  and 
stresses  are: 

V.  -  ,  =   +105.0  -  10  =   +95.0  [7,1/1  =   +95.0 

V2_  2  =   +105.0  -  20  -  2  X  10  =   +65.0  U,L2  =   +65.0 

V3_  3  =   +105.0  -2X20-3X10=   +35.0        U3L9  =   +35.0 

.  The  member  C74L4  cannot  be  easily  determined  by  passing  a 
section  4  —  4,  for  this  cuts  four  members.  It  is  determined  by  passing 
a  circular  section  about  the  point  L4,  the  equation  being  +  UtL4 
-  20.0  =  0,  from  which  U4Lt  =  +  20.0,  which  is  equal  to  the  dead 
panel  load  at  the  point  Z/4. 

The  live-load  chord  stresses  are  determined  by  multiplying  the 
dead-load  chord  stresses  by  the  ratio  of  the  live  to  the  dead  loads. 
This  has  been  found  to  be  equal  to  12.08.  The  live-load  chord  stresses 
are  found  to  be : 

L0L,  =  +182.0  UJJt=  -182.0 

L,L2  =  +312.0  UJJ3  =  -312.0 

L2L3  =  +390.0  U3U4  =  -390.0 

L3L4  =  +416.0 

As  the  character  of  the  stresses  which  can  be  taken  by  the 
diagonals  and  the  verticals  is  known,  the  maximum  and  minimum 
live-load  stresses  can  be  written  without  first  writing  the  stress 
equations.  The  maximum  live-load  stresses  are: 


BRIDGE  ENGINEERING 


53 


L0Ut  =  -218.4  X  1.302  =  -284.36  tf.L,  =  +218.4 

L,C72  =  -163.8  X  1.302  =  -213.27  U2L2  =  +163.8 

L2U3  =  -117.0  X  1.302  =  -152.33  U3L3  =  +117.0 

L3[74  =  -    78.0  X  1.302  =  -101.56  C74L4  =  +    78.0 

It  should  be  noted  that  when  L4  and  all  panel  points  to  the  right 
are  loaded,  the  shears  and  the  members  acting  are  as  shown  in  Fig. 
50.  The  dead-load  shear  on  the  section  4  —  4  is  +15.0,  less  the  load 
at  C74,  or  + 15.0  —  10.0  =  +5.0;  and  the  equation  of  stress  is  —  J74L4 
+  5.0  =  0,  from  which  J74L4  =  +5.0.  Thus  it  is  seen  that  in  this 


10 


10 


eo.o 


10 
U5 


10 


J     EO.O 
6S.4. 


eo.p 

6EA 


/ 


/ 


10 


d.l.v. 

+   15.0 

-  I5.O 

l.l.v. 

--    7.8 

+  15-6 

Total  v. 

+ 

+ 

d.l  v. 

+  ^-5.0 

+    15.0 

uUy 

—   7.8 

—   7.8 

Total  v. 

+ 

+ 

Fig.  50.  Fig.  51. 

Stress  Diagrams  for  Members  of  Howe  Truss  Span  of  Fig.  49. 

case  the  dead-load  stress  is  +5.0  when  the  live-load  stress  is  +78.0. 
The  maximum  stresses  in  the  counters  (see  Article  37)  are : 

(-46.8  +  15.0)  1.302  =   -41.4. 
The  minimum  live-load  stresses  are  now  written  as  follows: 


L,[7,  =   +    7.8  X  1.302  =   +10.16 
LM3  =   +23.4  X  1.302  =   +29.15 
LaU4  =  0 
UaLt  =  0 


17.L,  -  0 

C72L2  -   -7.8 

U3L3   (    See  discussion 

£/4L4    j        following. 


If  live  panel  loads  were  placed  at  points  Lv  L2,  and  L3  the  live- 
load  shear  in  c  —  c  would  be  —46.8;  and  the  dead-load  shear  being 
+ 15,  the  counter  would  act,  and  the  stress  in  U3L3  would  be  tensile 
and  equal  to  the  s'um  of  the  dead  and  live  panel  loads  which  are  at 
its  lower  end  Ly  If  points  LV  and  L2  had  live  panel  loads  on  them, 


63 


54  BRIDGE  ENGINEERING 

the  resultant  shear  in  c  —  c  would  be  —23.4  +  15.0  =  —8.4;  the 
counter  would  act,  and  the  stress  .in  U4L4  would  be  tensile  and  equal 
to  the  dead  panel  load  which  is  at  Ly  There  being  no  live  panel  load 
at  L3,  the  live-load  stress  in  U^  would  be  zero  under  this  loading. 
If  a  live  panel  load  be  placed  at  Ll  only,  then  the  shears  and  the  mem- 
bers acting  will  be  as  shown  in  Fig.  51,  and  V3.3  for  dead  load  = 
+  45.0  -  the  load  at  Uy  or  =  45  -  10  =•  +35.0.  The  F3.3  for 
live  load  =  —7.8,  and  the  stress  equation  —  U3L3  —  7.8  =  0,  from 
which  U3L3  =  —  7.8.  So  this  live-load  compression  stress  of  7  800 
pounds  occurs  at  the  same  time  as  the  dead-load  tensile  stress 
of  45  000  pounds. 

By  loading  various  groups  of  panel  points  in  succession  and 
determining  the  resulting  live-load  stresses  in  U4L4,  it  will  be  found 
that  under  no  loading  can  a  negative  live-load  stress  be  produced. 
The  minimum  live-load  stress  is  therefore  zero,  and  occurs  when 
there  is  no  live  load  on  the  bridge. 

The  stresses  should  now  be  placed  on  an  outline  diagram  similar 
to  that  of  Fig.  48,  and  the  stresses  in  corresponding  members  com- 
pared with  those  in  that  figure.  This  is  left  for  the  student. 

41.  Bowstring  and  Parabolic  Trusses.  A  bowstring  truss  is 
shown  in  Fig.  13,  the  full  lines  representing  the  main  members,  which 
are  the  members  under  stress  by  the  dead  load.  The  dotted  members 
represent  counters  which  may  be  stressed  by  the  action  of  the  live 
load. 

As  before  mentioned,  the  stresses  in  the  chords  and  also  in  the 
webbing  are  quite  uniform.  When  the  end  supports  and  the  panel 
points  lie  on  the  arc  of  a  certain  curve,  called  a  parabola,  then,  under 
full  load,  the  stresses  in  all  panels  of  the  lower  chord  are  equal;  the 
stress  in  all  verticals  is  tensile  and  is  equal  to  the  panel  load  at  the 
lower  end ;  and  the  stress  in  all  diagonals  is  zero.  Under  partial  load, 
the  stresses  in  the  webbing  are  exceedingly  small,  and  the  chord 
stresses  remain  almost  equal. 

If  it  is  desired  to  have  a  parabolic  truss,  first  decide  upon  the 
length  of  span,  the  number  of  panels,  and  the  height  at 
the  center.  The  height  of  any  vertical  post  is  given  by  the 
formula : 

k.H-  *™. 


BRIDGE  ENGINEERING 


which, 


All  distances  are  in  feet.  Suppose,  as  an  example,  that  it  was 
desired  to  determine  the  heights  of  the  vertical  posts  in  an  8-panel 
parabolic  truss  of  a  height  approximately  equal  to  24  feet.  One-half 


H  =  Approximate  height  at  center; 

d  =  Distance  of  vertical  post  from  center; 

I  =  Span; 

h  =  Height  of  vertical 


Fig.  52.    One-Half  of  8-Panel  Parabolic  Truss. 

the  truss  is  shown  in  Fig.  52.     At  the  center,  d  =  0,  and  the  equation 
reduces  to  h  =  H,  which  is  24  feet.     For  UgLv  d  =  20;  then, 


from  which, 
For  L\L2, 


h  =  24  -  4  X  3JX  20  t~ 
1602 

h  *=  22.5  feet. 


d  =  40 


h  =  24  -  4  X.24_X  402 


160 


For  l\Lv 


d  =  60 


h  =  24  -    4  X  j4  X 


h  =  18.0  feet. 


=  10.5  feet. 


Inspection  of  the  above  results  shows  that  the  span  or  the  center 
height  must  become  quite  great  before  the  clearance  at  UtL^  will  be 
sufficient  to  allow  the  traffic  to  pass  under  a  portal  bracing  at  this 
point.  For  this  reason  these  trusses  are  usually  built  as  through 
trusses  with  bracing  on  the  outside  of  the  truss,  which  connects  to 
the  floor-beams  extended. 


65 


56 


BRIDGE  ENGINEERING 


\ 


In  the  bowstring  truss, 
the  panel  points  of  the 
top  chord  usually  lie  on 
the  arc  of  a  parabola 
which  does  not  pass 
through  the  supports. 
For  example,  suppose 
that  it  was  decided  to 
have  the  span  and  pan- 
els the  same  as  shown  in 
Fig.  52,  but  the  height 
at  L1  was  to  be  '28  feet, 
and  at  L4  36  feet.  By 
substi  tu  ting  these  values 
in  the  equation  just 
given,  and  solving  for  I, 
the  place  will  be  deter- 
mined where  the  para- 
bolic curve  cuts  the 
lower  chord  extended, 
and  the  lengths  of  the 
vertical  posts  may  be 
computed  as  before. 
Substituting  these  re- 
sults : 


28  =  36  - 


4  X  36  X  602 


(-36  +  28)Z2  =  -  4  X36 
X  602 

I  =      /4  X  36  X  605 

"V  8 

=  254.5, 

which  shows  that  the 
arc  cuts  the  lower  chord 
extended  at  a  point 
254.5  -T-  2  =  127.25  feet 
from  the  center  of  the 
span  (see  Fig.  53). 


BRIDGE  ENGINEERING 


57 


The  other  vertical  posts  are: 

U3L3  h 


4  X  36  X  202 
36  -  —     ., , =  35.11  feetj 


U2L2 


254. 52 

4  X  36  X  402 

254.S2 


32.44  feet; 


h  =  36  -  —          =~j =  28.00  feet,  which  checks. 

254.5 


The  analysis  of  a  bowstring  truss  will  now  be  given.     Both  the 
maximum  and  minimum  stresses  will  be  determined,  as  reversal  of 


Fig.  54.    Outline  Diagram  of  5-Panel  Bowstring  Truss  Span. 

stresses  is  liable  to  occur  in  the  intermediate  posts.  The  loading  for 
minimum  live-load  stresses  can  be  ascertained  only  by  trial,  care 
being  taken  to  compute  the  dead-load  stresses  for  the  arrangement 
of  web  members  caused  by  that  particular  live  loading. 

Let  it  be  required  to  determine  the  maximum  stresses  in  the 
5-panel    100-foot  bowstring  truss 
shown    in   Fig.   54,   remembering  U, 

that  the  diagonals  take  only  ten- 
sion. The  height  of  U^  is  20 
feet,  and  of  U^  25  feet.  The 
dead  panel  load  is  17  200  pounds, 
and  the  live  panel  load  is  50  000 
pounds.  The  full  lines  show  the 
main  members  which  act  under 
dead-load  stress,  and  the  dotted 
lines  show  the  counters  which  may 

act  under  the  action  of  the  live  load.  One-third  of  the  dead 
panel  load,  or  5  730  pounds,  is  taken  as  acting  at  the  upper 
panel  points,  while  the  remainder,  11  470  pounds,  acts  at  the  lower 


L, 
11.47 

Fig.  55.    Resolution  of  Forces  around 

Panel  Point  in  Bowstring  Truss 

of  Fig.  54. 


67 


BRIDGE  ENGINEERING 


Fig:  61.  Fig.  62. 

Analysis  of  Stresses  in  Various  Members  of  the  Bowstring  Truss  of  Fig.  54. 


68 


BRIDGE  ENGINEERING 


59 


Fig.  66. 
Analysis  of  Stresses  in  Various  Members  of  the  Bowstring  Truss  of  Fig.  54. 


60  BRIDGE  ENGINEERING 

ones.  Articles  27,  28,  and  29  should  be  carefully,  reviewed  before 
going  further.  The  shear  times  the  secant  method  cannot  be  con- 
veniently employed  for  the  live-load  stresses  in  the  members  U^L2 
and  LJJ2,  as  the  section  will  cut  the  member  U^Lfv  and  the  vertical 
component  of  its  stress  must  be  reckoned  with  in  the  stress  equation 
The  method  of  moments  as  illustrated  in  Fig.  27,  Article  29,  will  be 
used  for  these  members. 

The  dead-load  reaction  is  2  X  17.2  =  +34.4.  The  dead-load 
chord  stresses  should  first  be  computed. 

By  resolving  the  horizontal  forces  around  Lv  it  is  seen  that  L0Lt 
=  LJj2  (see  Fig.  55).  Passing  the  section  a  —  a,  taking  the  center 
of  moments,  at  Uv  and  stating  the  equation  of  the  moments  to  the 
left  of  the  section,  there  results  (see  Fig.  56) : 

+  34.4  X  20  -  L,L2  X  20  =  0  .'.  L,L2  =   +34.4 

For  -LjL3,  the  section  b  —  b  is  passed ;  the  center  of  moments  is 
at  U2;  and  the  equation  of  the  moments  to  the  left  of  this  section 
(see  Fig.  57)  is: 
+  34.4  X  2  X  20  -  (11.47  +  5.73)  20  -  L2L3  X  25  =  0     .'.  L2L3  =  +41.26. 

By  passing  a  vertical  section  cutting  L^  and  L0UV  the  stress  in 
I/o^can  be  determined  by  taking  the  sum  of  the  vertical  forces  to 
the  left  and  equating  them  to  the  vertical  component  of  the  stress 
(see  Fig.  58).     The  equation  is: 
+  34.4  +  L0U1  X  0.707  =  0,  from  which  L0U1  =   -34.4  X  1.414  =  -  48.7. 

A  section  a  —  a  (Fig.  59)  shows  that  the  center  of  moments  for 
UJJ2  is  at  U2;  and  stating  the  moments  of  the  stress,  and  the  forces 
to  the  left  of  the  section,  there  results  an  equation  in  which  an 
unknown  lever  arm  enters.  This  lever  arm  I  is  readily  computed 
to  be  24.28  feet,  and  the  equation  can  now  be  written : 

+  34.4  X  2  X  20  -  (11.47  +  5.73)  20  +  UtU3  X  24.28  =  0 
.'.  U,U2  =   -42.51. 

The  stress  in  UZU3  is  determined  by  passing  a  vertical  section 
in  the  3d  panel,  and  taking  the  sum  of  the  horizontal  forces.  As  there 
is  no  dead-load  stress  in  the  members  L2U3  and  U^,  their  compo- 
nents will  be  zero.  Therefore  (see  Fig.  60)  it  is  evident  that  U2U3 
must  be  equal  and  opposite  to  L2L3  and  will  be  equal  to  —41.26. 

By  reference  to  Fig.  55,  the  stress  in  LJJl  is  seen  to  be  tensile  and 
equal  to  +11.47. 


BRIDGE  ENGINEERING  61 

Pass  a  circular  section  around  U2  and  take  the  sum  of  the  vertical 
components,  assuming  that  the  stress  in  U2L2  acts  away  from  the 
section.  The  length  of  UJJ2  is  1/52  +  202  -  20.6,  and  therefore  the 
vertical  component  of  UJJ2  will  be  (42.51  --  20.6)  X  5  -  10.32, 
which  acts  upward.  The  stress  equation  of  UyL2  (see  Fig,  61)  is: 

+  10.32  -  5.73  -  U2L2  =  0  .'.  U2L2  =   +4.59, 

showing  that  a  tensile  stress  occurs  in  U2L2  when  all  panel  points  are 
loaded. 

The  simplest  method  of  ascertaining  the  stress  in  UtL2  is  to  pass 
a  vertical  section  cutting  members  as  shown  in  Fig.  62,  and  to  equate 
the  horizontal  forces  and  stresses.  The  horizontal  component  of 
UlU2is: 

45*    X  20  =  41.30,  which  acts  to  ward  the  left. 


The  equation  of  stress  is,  then: 

-41.30  +  34.40  +  U,L2  sin  <j>  =  0;  but  sin  0  =  0.707; 
U,L2  =   +6.90  X  1.414 

=   +9.76 

All  the  dead-load  stresses  being  computed,  the  next  operation 
will  be  to  determine  the  live-load  chord  stresses.  These  are  pro- 
portional to  the  dead-load  stresses  in  the  same  ratio  as  the  live  panel 
load  is  to  the  dead  panel  load.  This  ratio  is  50  H-  17.2  =  2.907, 
and  the  chord  and  end-post  live-load  stresses  are: 

L0U,  =   -48.71  X  2.907  =  -141.7 

UtU2  =   -42.51  X  2.907  =  -123.6 

U2U3  =   -42.26  X  2.907  =  -123.0 

L0L2  =   +34.40  X  2.907  =  +100.2 

L2L3  =   +41.26  X  2.907  =  +120.3 

Also,  the  stress  in  U2L2  when  the  live  load  covers  the  entire  bridge 
is  not  2.907  X  4.59,  as  it  must  be  remembered  that  part  of  the  dead 
load  is  at  the  panel  points  of  the  upper  chord.  Taking  a  circular 
section  around  U2  (see  Fig.  61),  and  noting  that  there  is  no  load  at  U2, 
it  is  seen  that  the  stress  in  U2L2  due  to  live  load  is  simply  equal  to  the 
vertical  component  of  the  live-load  stress  of  UjU2  and  wjll  be  tensile. 
It  is: 

U1U2  =  (123.6  -f-  20.6)  X  5  =   +30.0. 

The  maximum  live-load  stress  in  U1Ll  is  tensile,  and  equal  to 
the  live  panel  load  at  L1  (see  Fig.  55). 


71 


25 
+  30.0-  t/jLs  cos  0=0;  but  cos  <£  =  =0.782; 


02  BRIDGE  ENGINEERING 

To  obtain  the  maximum  stress  in  U^,  load  L3  and  L4.    The 

erv 

shear  V3  will  then  be  ^  (1-f  2)  =  +30.0.     The  section  will  cut 
o 

the  members  as  shown  in  Fig.  63,  and  the  equation  of  stress  will  be  : 

J 

/.  t/^3  =  +38.4. 

If  panel  points  L^  and  L2  were  loaded,  it  is  evident  that  the  stress 
in  L2U3  would  be  +38.4. 

To  obtain  the  maximum  live-load  stress  in  UJLi2,  a  section  is 
passed  cutting  UJJV  L^,  and  U^  (Fig.  64).  The  center  of 
moments  will  be  at  the  intersection  of  UJJ2  and  L}L2,  and  this  point 
lies  some  place  to  the  left  of  the  support  L0.  The  lever  arm  of  U:LZ 
will  be  the  perpendicular  distance  from  this  point  to  the  line  UVLZ 
extended.  The  panel  points  L2,  L3,  and  L^  are  loaded.  The  left 

50 

reaction  is  then  (1  +  2  +  3)  —  -  +  60.0.      The  lever  arms  are 
5 

easily  computed,  and  these,  together  with  the  members  cut,  are  shown 
in  Fig.  64.     The  equation  of  stress  is: 

-  60.0  X  GO.O+t/jLaX-TO.S  =  0  .-.  U,L2=  +50.80. 

If  a  load  were  put  on  Ll  only,  then  the  reaction  at  L0  would  be 
4 
—  X  50  =  40;  and  the  equation  of  stress  would  then  be: 

O 

-40.0  X  60.0  +  50  X  (60.0  +  20.0)  +  t/,L2  X  70.8  =  0  .'.  J7,L2  =  -22.6. 
As  this  is  compression  and  greater  than  the  dead-load  stress,  +  9.76, 
a  counter  is  required  in  that  panel.  In  order  to  get  the  stress  in  the 
counter,  it  must  be  inserted,  U^  being  left  "out,  and  the  dead  and 
live  load  stresses  computed  and  their  difference  taken.  Fig.  65  gives 
the  lever  arms,  center  of  moments,  and  the  forces  acting  in  this  case. 
The  dead-load  stress  is: 

-34.4  X  60.0  +  (11.47  +  5.73)  (60  +  20)  -  L,C72  X  62.5  =  0 
.'.  L,U2  =   -11.02; 

and  the  live-load  stress  is: 

-40  X  60  +  50  (60  +  20)  -  L.O,  X  62.5  =  0  .-.  L,U2  =   +25.60, 

and  the  stress  in  the  counter  is  the  algebraic  sum  of  these  two,  or 
-11.02  +  25.60  =  +14.58. 


72 


BRIDGE  ENGINEERING 


03 


When  a  live  panel  load  is  at  Lv  LJJ2  is  acting,  as  has  just  been 
proved.  As  this  load  at  Lt  causes  a  negative  shear  in  all  panels  to 
the  right,  this  negative  shear  in  the  center  panel  will  cause  L2U3  to 
act.  A  section  may  now  be  passed  as  shown  in  Fig.  66,  and  the  stress 
equations  for  U2L2  written: 

For  dead  load,  +34.4  -  11.47  -  2  X  5.73  -  U2L2  =  0  .'.  U2L2  =-  ,11.47 
For  live  load,  +40.0  -  50.0  -  U2L2  =  0  .'.  U2L2  =  -10.00 

Total  =   +    1.47 

This  is  evidently  not  a  maximum  for  U^L^  for  when  a  full  live  load 
was  on  the  span,  the  stress  was  +30.0  due  to  live  load  and  +4.59 
due  to  dead  load. 

It  might  be  well  to  consider  what  effect  is  produced  by  loading 
L3  and  L4.  The  loading  of  L2  and  Ll  need  not  be  considered,  since 
it  is  evident  that,  as  this  causes  the  total  shear  in  panel  2  to  be  positive 
and  the  total  shear  in  panel  3  to  be  negative,  therefore  U^  and  L2U3 


Fig.  68.    Stress  Diagram  of  Half -Span  of  Parabolic  Truss  of  Fig.  54. 

will  act,  and  this  causes  a  tensile  stress  in  U2L2  equal  to  the  vertical 
components  of  the  dead  and  live  load  stresses  in  UJJ2  less  the  dead 
panel  load  at  U2.  With  a  live  panel  load  at  L3  and  Lv  the  left  reaction 

50 

is  — •  (1  +  2)  =  +30.0.  The  section,  the  live-load  forces,  the  cen- 
ter of  moments,  and  the  members  acting  are  shown  in  Fig.  67.  The 
dead-load  stress  in  U2L2  will  be  the  same  as  when  the  truss  has  no 
live  load  on  it.  The  stress  equation  for  the  live  load  is: 

-60  X  30  -  (60  +  20  +  20)  X  L2C72  =  0  .'.  L2U2  =   -18.0. 


04 


BRIDGE  ENGINEERING 


The  dead-load  stress  being  +4.59,  this 
stress  of  — 18.0  causes  a  reversal  of  stress 
in  the  vertical.  For  this  reason  the  ver- 
ticals of  bowstring  trusses  are,  like  web 
members  of  Warren  trusses,  built  so  as 
to  take  either  tension  or  compression. 
The  minimum  stresses  in  the  diagonals 
will  be  zero,  for  when  one  diagonal  in  a 
panel  is  acting,  the  other  is  not. 

The  diagram  of  half  of  the  truss  in  Fig. 
68  gives  all  the  stresses. 

It  is  to  be  noted  by  the  student,  that 
in  some  cases  one  method  for  the  deter- 
mination of  s tresses  is  preferable  to  others 
in  that  it  saves  labor  of  computation. 
The  analysis  of  the  truss  of  Fig.  68  illus- 
trates this  fact. 

42.  The  Baltimore  Truss.  Baltimore 
trusses  are  of  two  classes — those  in  which 
the  half-diagonals,  called  sub-diagonals, 
are  in  compression,  and  those  in  which 
the  sub-diagonals  are  in  tension.  The 
latter  class  is  the  one  most  usually  built, 
as  it  is  more  economical  on  account  of 
many  of  its  members  being  in  tension,  in 
which  case  these  members  are  cheaper 
and  easier  to  build  than  if  they  were  com- 
pression members.  Fig.  14  shows  boiii 
types  of  truss.  The  Baltimore  truss  does 
not  have  a  simple  system  of  webbing,  and 
tbi  that  reason  the  analysis  is  here  pre- 
sented. As  the  tension  sub-diagonal  truss 
is  the  type  in  most  common  use,  its  analy- 
sis will  be  given. 

Let  it  be  required  to  compute  the 
maximum  stresses  in  the  14-panel  280- 
foot  span  of  Fig.  69.  The  height  is  40 
feet,  the  dead  panel  load  24  000  pounds, 


d     o 

*  a 


74 


BRIDGE  ENGINEERING  65 

and  the  live  panel  load  40  000  pounds.  One-third  of  the  dead 
panel  load  is  applied  at  the  upper  ends  of  the  long  verticals  and  also 
of  the  half-verticals.  These  half-verticals  are  designated  as  sub- 
verlicals.  Attention  is  called  to  the  system  of  notation  used  for  the 
ends  of  the  sub-verticals.  The  full  lines  in  Fig.  69  represent  the 
main  members,  being  stressed  by  dead  load  only.  The  heavy  lines 
indicate  those  members  that  take  compression,  the  light  lines  those 
that  take  tension,  and  the  broken  lines  the  counter-braces.  In  this, 
as  in  nearly  all  Baltimore  trusses,  the  diagonals  make  an  angle  of  45 
degrees  with  the  vertical. 

The  dead  and  the  positive  live-load  shears  in  the  various  panels 
should  be  computed.  They  are : 

DEAD-LOAD  V  +  LIVE-LOAD  V 

7,      +156.00  Vl  =  (1  +   13)  |j  =   +260.00 

40 
V2     + 132.00  V2  =  (1  +   ....  12)  ^  =   +223.00 

V3     +108.00  V3  =  (1  +  11)^- =  +188.50 

Vt     +   84.00  Vt  =  (1  +   10)  Y     =   + 157.20 

75     +   60.00  V5  =  (1  +   .  .  .  .    9)  -p     =   + 128.50 

V6     +   36.00  V0  =  (1  +   ....    8)  YJ-  =   + 102.80 

40 
V7     +    12.00  Vj  =  (1  +   7)  ~  =   +    80.00 

It  is  only  necessary  to  determine  the  negative  live-load  shear  in 
panels  5  and  7,  in  order  to  ascertain  if  there  is  a  counter  required. 
These  shears  are : 

-  Vs  =  (10  +  11  +  12+  13)  ~  -  4  X  40  =   -28.60 

-  F7  =  (8  +  9  +  10  +  11  +  12  +  13)  ~  -  6  X  40  =   -60.00 

From  a  comparison  of  these  with  the  dead-load  shears,  it  is  seen 
(see  Article  37)  that  a  counter  is  required  in  panel  7  only. 

The  dead-load  stresses  are  first  to  be  computed.  The  stress  in 
any  sub-vertical  is  found  by  passing  a  circular  section  around  its 
lower  end,  and  equating  the  sum  of  the  vertical  forces,  assuming 
in  this,  as  in  all  cases,  that  the  unknown  stress  acts  away  from  the 


75 


BRIDGE  ENGINEERING 


section.  Take  Mlmv  for  example.  Fig.  70  gives  the  section,  the 
forces  acting,  and  the  members  cut.  Then, 

+  M,w1  -  16.0  =  0  .'.  M1m1  =   +16.0 

As  all  sub-verticals  have  the  same  dead  load  at  their  lower  end,  it 
follows  that  the  dead-load  stress  in  all  sub-verticals  is  the  same,  a 
tensile  stress  of  16  000  pounds. 

The  dead-load  stresses  in  the  sub-diagonals  are  determined  by 
resolving  the  forces  around  the  joint  at  their  lower  end.  The  com- 
ponents perpendicular  to  the  diagonal  are  taken  (see  Fig.  71).  Take 


M, 

16.0 

Fig.  70.    Diagram  for  Calculating  Stress  in 
Sub- Vertical  of  Baltimore  Truss. 

m2U2.  The  known  forces  or 
stresses  are  the  dead  panel  load 
of  8.0  and  the  stress  in  w2M2, 
which  is  16.0  and  which  being 
tensile  acts  away  from  the  sec- 
tion. The  stress  equation  is : 

+  m2U2  -  8.0  sine  (f>  —  16.0  sine  $  =  0. 
<£  =  45°,  sine  <£  =  0.707,and 
m2U2  -  8.0  X  0.707  -  16.0  X  0.707  =  0 
.-.  m2U2  =   +16.96. 

This  equation  may  be  put  in  another  form  by  multiplying  and  dividing 
the  numerical  values  bv  2: 


Fig.  71.    Diagram  for  Calculating  Stress  in 
Sub-Diagonal  of  Baltimore  Truss. 


(8.0  +  16.0) 


X  1.414  =  0; 


or, 


m,P,-+% 


which  proves  the  well-known  saying  that  the  stress  in  the  sub-diagonals 
is  equal  to  one-half  the  panel  load,  times  the  secant  of  the  angle  (f>.  It 
also  shows  that  the  vertical  component  of  the  sub-diagonal  is  equal  to 


BRIDGE  ENGINEERING 


67 


in 


one-half  the  panel  load.     This  fact  should  be  remembered,  as  it  will 
be  frequently  used  further  on. 

In  a  similar  manner,  the  stress  in  all  the  tension  sub-diagonals 
will  be  found  to  be  the  same,  + 16.96,  and 
the  stress  in  the  compression  sub-diagonal 
m^Li  is  -16.96. 

The  stress  in  the  member  L0ml  and  in 
the  upper  half  of  any  main  diagonal  (i.  e., 
Ujin^  U2m3,  and  Ugn^)  is  determined  as  in 
the  diagonals  of  the  Pratt  or  Howe  truss, 
for  the  section  passed  cuts  but  one  mem- 
ber, which  has  a  vertical  component.  Take 
^TO,  (see  Fig.  72).  Then  +156.0  +  L0ml 


156.0 


Fig.  72.    Stress  in  Diagonal 
of  Baltimore  Truss. 


cos  45°  =  0,  from  which  i0w1  =  —220.5.  For  Ujtn2  the  section  is 
passed  as  in  Fig.  73,  and  the  equation  of  stress  is  +  V3  —  t/,m2  cos 
45°  =  0,  or  +108.0  -  U^  X  0.707  -  0,  from  which  Lr,m2  - 
+  152.9. 

In  a  similar  manner, 

U2m3  =   +60.0  -f-  0.707  =   +84.84; 

U3mt  =   + 12.0  -i-  0.707  =   + 16.96. 

The  stresses  in  mJJv  mJLv  and  w3L3  may  be  determined  by 


Fig.  73.    Stress  in  Upper  Half  of  Main 
Diagonal  of  Baltimore  Truss. 


Fig.  74.    Stress  in  Diagonal  of  Baltimore 
Truss. 


resolving  the  forces  about  TO,,  mv  and  TOS;  but  a  neater  solution  is  to 
pass  a  vertical  section  cutting  the  member  whose  stress  is  desired, 
and  to  equate  to  zero  the  shear  and  the  vertical  components  of  all 


77 


68 


BRIDGE  ENGINEERING 


the  members  cut  (see  Fig.  24,  Article  28).     The  section  for 
passed  as  in  Fig.  74.    The  equation  of  stress  is  then: 
m1U1  cos  45°  +  mA  cos  45°  +  F2  =  0; 


but  the  vertical  component  of 


is—  =  12;  and  therefore, 


mlUl  X  0.707  +  12  +  132  =  0 
.-,mlUl  =  -203.6. 

For  w2L2,   the  section  is  as  shown  in  Fig.  75,  and  the  stress 

equation  is  : 

-m.zL2  X  0.707  +  vert,  component  m2U2  +   K4  = 
-m2L2  X  0.707  +  12  +  84  =  0 
.-.  m2L2  =  +  135.6. 


[Fig.  75.    Calculating  Stress  in  Lower  Half-Diagonal  of  Baltimore  Truss. 

In  a  similar  manner,  passing  a  section  cutting  U2U3,  m3U3,  m^, 
and  MjLg,  the  stress  equation  may  be  written: 
-  m3L3  X  0.707  +  12  +  36  =  0 
.-.  m3L3  =  +67.85. 

The  stresses  in  the  verticals  are  best  determined  by  resolving 
the  vertical  forces  at  their  lower  end.  Referring  successively  to 
diagrams  a,  b,  and  c  of  Fig.  76,  the  stress  equations  are: 

+  U1L1  -  16.0  -  12.0  =  0  .'.  t^L,  =  +28.0 

+  f/2L2  -  16.0  +  96.0  =  0  .'.  U2L2  =   -80.0 

+  C73L3  -  16.0  +  48.0  =  0  .'.  U3L3  =  -32.0 

96  and  48  being  the  vertical  components  of  mJL2  and  m3L3  respec- 
tively. 


78 


BRIDGE  ENGINEERING 


69 


The  chord  stresses  are  easiest  computed  by  considering  the 
resolution  of  horizontal  forces  at  the  panel  points.  As  the  diagonals 
make  an  angle  of  45°  with  the  vertical,  their  horizontal  and  vertical 


16.0  16.0 

Fig.  76.    Calculating  Stresses  in  Verticals  of  Baltimore  Truss  of  Fig.  69. 

components  are  equal.  For  instance,  the  horizontal  component  of 
the  members  Ljn^  Ujm2,  and  U2m3  are  equal  to  the  shear  in  that 
panel,  which  is  their  vertical  component.  At  point  L0  (see  Fig.  77), 
there  results: 

+  L0A/i  —  horizontal  component  of  M ^L0  =  0;  or, 

+  L0M,  -  156  =  0 

.-.  L0M,  =  +156.0; 

and  from  Fig.  70  it  is  evident  that  L0Mt  =  MJjr    At  point  Ll  (see 
Fig.  78),  LtM2  is  equal  to  M1LV 
less  the   horizontal  component  of 
MJjv  and  the  equation  is: 

- 156  +  12   +  L,Af2  =  0 
.  L,Af2  =  + 144.0;  and  M2L2=  + 144.0. 

At  point  L2  (see  Fig.  79),  L2M3 
is  equal  to  the  sum  of  the  horizon- 
tal components  of  M^L2  and  m2L2; 
that  is, 


+  L2M3  -  144.0  -  96.0  =  0 
.-.  L2M3  =  M3L3  =   +240.0. 


Fig.  77.    Chord  Stress  in  Baltimore  Truss. 


In  a  similar  manner,  at  point  L3,  the  stress  equation  is: 


+  L3M4  -  240.0  -  48.0  =  0 

.-.  L3M4  =  MtL4  =   +288.0. 


there  results  the 


At  the  upper  panel  point  Ul  (see  Fig. 
equation:  % 

+  Z/il72  +  hor.  comp.  C7,m2  +  hor.  comp.  mlU1  =  0; 
U,U2  +  108.0  +  144  =  0;    or,  U,U2  =   -252.0. 

For  the  member  U2U3  (see  Fig.  81),  the  equation  is: 


79 


70 


BRIDGE  ENGINEERING 


+  UJJZ  +  U2U3  -  hor.  comp.  m2C/2  +  hor.  comp.  U2ma  =  0 
+  252.0  +  U2U3  -  12  +  60  =  0 
/.  U2U3  =   -300.0. 

In  a  similar  manner,  by  resolving  the  horizontal  forces  at  U3,  it 
will  be  seen  that  the  action  of  m3U3  will  neutralize  that  of  U3mt,  us 


M, 


L  . 

Fig.  78.  Fig.  79. 

Bottom  Chord  Stresses  in  Baltimore  Truss. 

they  are  equal  and  pull  in  opposite  directions,  and  U3U4  is  equal  to 


The  live-load  stresses  in  the  chords,  the  end-post,  and  the  sub- 
diagonals  are  all  proportional  to  the  dead-load  stresses  in  the  same 


Fig.  80.  Fig.  81. 

Top  Chord  Stresses  in  Baltimore  Truss. 

ratio  as  the  live  panel  load  is  to  the  dead  panel  load.     This  ratio  is 

40 

—  =  1.667.  By  reference  to  Fig.  70,  it  will  be  seen  that  the  live- 
load  stress  in  the  sub-verticals  is  +40.0  for  each  one.  The  following 
stresses  can  now  be  determined : 

L0ml   =    -220.5  X  1.667  =   -367.5 
,t/,  =   -203.6  X  1.667  =   -339.5 


U,U2  =  -252.0  X 
f/2C7,  =  -300.0  X 
U3Ut  =  -300.0  X 


L0L,    =  +156.0  X  1.667  =   +260.0 


L,L2  =  +144.0  X 
L2L3  =  +240.0  X 
L3L4 


.067  =  -420.0 
.667  =  -500.0 
.667  =  -500.0 


.667  =   +240.0 
.667  =   +405.0 
+288.0  X  1.667  =   +481.0 


80 


BRIDGE  ENGINEERING 


71 


m.L,  =  -    16.96  X  1.667  =    -   28.28 
m,Us  =  m3U3  =   +16.96  X  1.667  =   +28.28 

The  vertical  U^  will  have  its  maximum  live-load  stress  when 
points  J/t  and  L1  are  loaded,  for  these  are  the  only  loads  which  cause 
a  stress  in  that  member  (see  Fig.  76a).  The  equation  is: 


-  ~  -  40  + 


=  0, 


from  which, 
t/jL,  =   +60.0. 

The  maximum 
live-load  stresses 
in  Ujm2,  U2m3,  and 
U3m4  are  obtained 
in  a  manner  exact- 
ly like  that  used 
in  obtaining  dead- 
load  stress,  only 
the  live-load  posi- 
tive shear  is  used. 
The  stresses  are: 


Stress  in  Lower  Half  of  Main  Diagonal  of  Baltimore 
Truss. 


U}m2  X  0.707  +  188.5  =  0 
U2ma  X  0.707  +  128.5  =  0 
U 3mt  X  0.707  +  80.0  =  0 


.'.  U,m2  =  +2665 
.  .  U2ma  =  +181  5 
.-.  U.ni  =  +113.1 


In  the  determination  of  the  maximum  live-load  stress  in  the 
lower  halves  of  the  main  diagonals,  ra^,  ra^,  and  m4Z4,  one  of  the 
peculiarities  of  this  truss  becomes  apparent.  A  section  being  passed 
as  in  Fig.  82,  the  panel  point  ahead  of  the  section,  and  all  between 
the  section  and  the  right  support,  must  be  loaded.  This  of  course 
produces  a  stress  in  ra2?72,  and  the  vertical  component  of  this  enters 
the  stress  equation.  The  shear  in  the  section  a  —  a  under  this  load- 
ing is: 

Va_a  =   +188.5  -  40  =   +148.5; 

and  the  stress  equation  is: 

-m2L2  X  0.707  +  ~  +  148.5  =  0 

.-.  m2L2  =   +238.0. 

If  the  truss  had  been  loaded  from  the  section  to  the  right,  there  being 
no  load  on  M2,  no  stress  would  result  in  m2U2,  and  the  stress  in 


81 


72 


BRIDGE  ENGINEERING 


would  have  been 


157.2 
0.707 


=  +222.2.     In  a  similar  manner, 


Fig.  83.    Stress  in  Main  Vertical  of  Baltimore  Truss. 


by  loading  successively  points  M3  and  to  the  right,  and  M4  and  to 
the  right,  the  stress  equations  of  m3L3  and  m4L4  are: 

-m3L3  X  0.707  + -y  +  128.5  -  40  =  0  .'.  maL3  =   +153.3 

-w4L4  X  0.707  +  ~  +     80.0  -  40  =  0  .'.  m4L4  =   +   84.8 

The  maximum  live-load  stresses  in  the  main  verticals  occur  when 
the  panel  points  to  the  right  of  the  section  which  cuts  the  member 

under  considera- 
tion are  loaded. 
There  being  no 
load  at  the  end  of 
the  sub-vertical 
just  to  the  left  of 
the  section,  there 
will  be  no  stress 
in  the  sub-diag- 
onal which  the  sec- 
tion cuts.  The  chords,  of  course,  do  not  exert  a  vertical  com- 
ponent; and  so  the  only  unknown  term  of  the  stress  equation  is  the 
stress  in  the  member  itself.  Fig.  83  shows  how  the  section  should 
be  passed  when  U^L2  is  considered.  The  stress  equation  is: 
+  U2L2  +  Fa_a  =  0;  +  U2L2  +  128.5  =  0;  .'.  U2L2  =  -128.5. 

In  a  similar  manner,  by  passing  a  section  cutting  U2U3,  m3U3, 
C/gZj,  L3mv  and  loading  M4  and  to  the  right,  it  is  seen  that  the  stress 
equation  for  U3L3  is: 

+  UaLa  +  80.0  =  0  .'.  U3L3  =   -80.0 

The  components  of  m3U3  and  L3m4  are  zero,  as  can  readily  be  proved 
by  solving  for  them  under  this  loading. 

Fig.  84  gives  all  the  stresses,  and  they  are  written  in  order  of 
dead  load,  live  load,  and  maximum. 

43.  Other  Trusses.  The  analysis  of  the  foregoing  trusses  will 
enable  one  to  solve  any  of  the  trusses  of  modern  times.  For  the 
solution  of  the  Whipple  (sometimes  called  the  "double-intersection 
Pratt")  and  others  which  are  not  mentioned  in  this  text,  the  student 


BRIDGE  ENGINEERING 


73 


is  referred  to  the  text- 
books of  F.  E.  Tur- 
neaure  and  Mans- 
field Merriman. 

ENGINE  LOADS 

44.     Use  of  En= 
gine  Loads.    It  was 

formerly  the  custom 
for  railroads  to  spec- 
ify that  the  engine  to 
be  used  in  computing 
the  stresses  in  their 
bridges  should  be  one 
of  their  own  which 
was  in  actual  use. 
The  engines  of  differ- 
ent roads  were  usual- 
ly different  both  in 
regard  to  the  weight 
on  the  various  wheels 
and  in  regard  to  the 
number  and  spacing 
of  the  wheels.  Of 
late  years,  consider- 
able progress  has 
been  made  towards 
the  adoption  of  a 
typical  engine  load- 
ing as  standard. 
These  typical  engines 
(see  Fig.  17,  Article 
25)  vary  only  in  re- 
gard to  the  weights 
on  the  wheels,  the 
number  and  spacing 
of  wheels  being  the 
same  in  all  engines. 


71 


BRIDGE  ENGINEERING 


«Ti 

vO  ci, 
<  3' 

O~ 
& 


The  distance  between  wheels  is  an 
even  number  of  feet,  instead  of  an  odd 
number  of  feet  and  inches  and  frac- 
tions thereof.  For  examples  of  load- 
ings which  are  in  almost  universal  use, 
consult  the  specifications  of  Cooper  or 
Waddell. 

The  labor  of  computation  of  stresses 
when  engine  loads  are  used  is  consid- 
erably lessened  by  the  use  of  the  so- 
called  engine  diagrams.  Fig.  85  gives 
a  diagram  which  has  been  found  very 
convenient.  The  first  line  at  the  top 
represents  the  bending  moment  of  all 
the  loads  about  the  point  to  the  right 
of  it.  All  the  loads  are  given  in  thou- 
sands of  pounds,  and  all  the  moments 
are  in  thousands  of  pound-feet.  The 
practice  of  writing  results  in  thousands 
of  pounds — or,  in  case  of  moments,  in 
thousands  of  pound-feet  or  pound- 
inches — is  to  be  recommended,  as  it 
saves  the  unnecessary  labor  of  writing 
ciphers.  Throughout  this  text  this 
practice  has  been  extensively  followed, 
the  stresses  being  written  to  the  near- 
est ten  pounds  or  one-hundred  pounds 
as  the  case  may  be.  For  example, 
6  433  may  be  written  6.43  or  6.4,  the 
few  pounds  which  are  neglected  mak- 
ing no  appreciable  difference  in  the 
design.  The  distances  are  in  feet. 

As  an  example  of  the  use  of  the  first 
line  at  the  top,  suppose  that  it  is  de- 
sired to  find  the  moment  of  all  the 
loads  to  the  left  of  a  certain  point 
when  wheel  6  (the  numbers  of  the 
wheels  are  placed  inside  of  the  circles 


84 


BRIDGE  ENGINEERING  75 

representing  the  wheels)  is  just  over  the  point.  The  moment  will 
be  1  640  000  pound-feet,  which  is  obtained  by  reading  off  the  1  640 
just  to  the  right  of  the  line  through  wheel  6. 

When  using  the  first  line  for  values  at  sections  in  the  uniform 
load,  the  values  given  represent  the  moment  of  all  wheel  and  uniform 
loads  about  the  points  in  the  line  or  section  to  the  left  of  the  value 
given.  For  example,  if  it  is  desired  to  find  the  moment  about  a 
point  in  line  2,  it  will  be  19  304  000  pound-feet,  the  value  19  304 
appearing  to  the  right  of  the  line. 

The  line  of  figures  below  the  wheels  indicates  the  distances 
between  any  two  wheels. 

The  third  line  of  figures  indicates  the  distance  from  the  first 
wheel  to  the  wheel  to  the  right.  For  instance,  37  is  the  distance  from 
wheel  1  to  wheel  7, 

The  values  in  the  fourth  line  indicate  the  sum  total  of  all  the 
loads  to  the  left  of  the  value  given.  For  example,  245  signifies  that 
the  loads  1  to  15  inclusive  weigh  245  000  pounds. 

The  values  in  lines  5  and  6  are  similar  to  those  of  lines  3  and  4, 
except  that  the  starting  point  is  at  the  head  of  the  uniform  load. 
For  example,  40  in  line  5,  and  112  in  line  6,  indicate  that  it  is  40  feet 
from  the  head  of  the  uniform  load  to  the  wheel  12,  and  that  wheels 
18  to  13  inclusive  weigh  112000  pounds. 

The  values  in  lines  7  to  16  indicate  the  value  of  the  moment  of 
all  the  wheels  from  the  zigzag  line  up  to  and  including  the  one  to  the 
left  or  the  right,  according  as  the  value  is  to  the  left  or  the  right  of 
the  zigzag  line.  For  example,  2  745,  line  11,  indicates  that  the 
moments  of  wheels  8  to  14  inclusive  about  the  zigzag  line  just  under 
wheel  15,  is  2  745  000  pound-feet;  or  the  value  1  704,  line  14,  shows 
that  the  moments  of  wheels  13  to  18  about  the  zigzag  line  just  under 
wheel  12  is  1  704  000  pound-feet. 

When  line  4  of  figures  is  under  the  uniform  load,  the  values  refer 
to  the  vertical  line  to  the  right; 'thus  324  is  the  value  of  all  loads  to 
the  left  of  line  3  about  that  line. 

For  values  of  moments  at  points  which  fall  in  between  wheels, 
or  at  positions  in  the  uniform  load  where  the  value  of  the  moment 
is  not  given,  a  very  important  principle  of  applied  mechanics  is  used. 
It  is: 

Ma  =  M'  +  Wx  +.        , 


85 


76 


BRIDGE  ENGINEERING 


in  which, 

M,  =  Moment  at  section  desired; 
M '   =  Value  of  moment  at  preceding  vertical  line; 
W    =  Sum  total  of  all  loads  to  the  left  of  and  at  the  point  where  M' 

is  taken; 
x    —  Distance  from  section  under  consideration  to  vertical  line  to 

which  M'  is  referred; 
w    =  Uniform  load  on  the  distance  x. 

Let  it  be  desired,  for  example,  to  determine  the  moment  at  a 
a  point  c,  3  feet  to  the  right  of  wheel 

13.     The  position  of  the  loads  is 
given  in  Fig.  86.     The  moment  is: 

M...  =  7  668  +  212  X  3 

=  7  668  +  636 

=  8  304  =  8  304  000  pound- 
feet,  there  being  no  uni- 
form load. 

To  illustrate  the  method  when 
applied  to  points  in  the  uniform 
load,  assume  the  point  to  be  7  feet 
to  the  right  of  line  2.  The  po- 
sition is  illustrated  in  Fig.  87.  The 
moment  is: 


eo 


6708 


eo 


74' 


7668 


Jft.- 


79' 


eo 


ese 


Fig.  86.   Calculation  of  Moment  at  a  Point 
under  Engine  Load. 


Mb-b  =  19  304  +  304  X  7  +  7"  X  2. 

=  21  481  =  21  481  000  pound-feet. 

The  use  of  the  moment  diagram  is  now  apparent.  Reactions 
due  to  any  position  of  the  engines  may  be  determined  by  dividing  the 
span  into  the  value  obtained  for  the  moment  at  the  right  end  of  the 
span.  Likewise,  if  the  moment  of  the  reaction  about  any  panel  point 
is  determined  and  from  it  the  moment  of  the  wheel  loads  about  that 
same  panel  point  are  subtracted,  then  the  result,  divided  by  the 
height  of  the  truss,  will  give  the  chord  stress.  For  example,  if  the 
right  end  of  an  8-panel  196-foot  span  truss,  height  25  feet,  came  7 
feet  to  the  right  of  the  vertical  line  2,  then  the  moment  at  this  point 
(see  Fig.  87)  would  be  21481000,  and  the  reaction  would  be 
21  481  000  -  196  -  109  600.  This  position  of  the  loads  would 
cause  the  panel  point  L6  to  come  3  feet  to  the  right  of  wheel  13.  The 
moment  of  the  reaction  about  LR  is  109  600  X  6  X  24.5  =  16  111  200; 


88 


BRIDGE  ENGINEERING 


77 


and   the   chord   stress    U6L6   for  this    position  of    the  engine   is: 
16111200-8304000 


25 


-31 2  000  pounds. 


In  using  the  engine  to  determine  the  shear  in  any  particular 
panel,  it  must  be  remembered  that  the  shear  is  not  the  left  reaction 
less  all  the  loads  to  the  left  of  the  panel  point  on  the  right  of  the 
section,  as  the  loads  in  the  panel  under  consideration  are  carried  on 
stringers,  and  these  stringers  transfer  a  portion  of  the  loads  to  the 


163  64 


19304 


eo 


7ft. 


eo 


2000  lt>s.  per  L 


5' 


10' 


10' 


109' 


119' 


304 


Fig.  87.    Calculation  of  Moment  at  Point  under  Uniform  Load. 

panel  point  on  the  left  of  the  panel,  and  a  portion  to  the  panel  point 
on  the  right  of  the  panel.  Only  that  portion  of  the  loads  in  the  panel 
which  is  transferred  to  the  left  panel  point  should  be  subtracted  from 
the  reaction,  as  should  all  of  the  loads  to  the  left  of  the  panel  under 
consideration.  If,  in  a  6-panei  120-foot  span  Pratt  truss,  the  wheel 
6  comes  at  L2,  the  left  reaction  will  be  : 


Rl  =  120 


284 


=  143-6; 


and  the  loads  in  the  first  two  panels  will  be  in  position  as  indicated 
by  Fig.  88,  the  wheel  3  being  1  foot  to  the  right  of  point  Lr  Let  it 
be  required  to  determine  the  shear  in  the  panel  LtL2  when  the  loads 
are  in  this  position.  It  will  be  the  reaction  143.6  minus  loads  1  and 
2  and  also  that  portion  of  the  loads  3,  4,  and  5  which  will  be  trans- 
ferred by  the  stringers  to  -the  point  Lr  As  the  stringers  are  simple 


87 


BRIDGE  ENGINEERING 


G 
G 

G 
-6 


Fig.  89.    Shear  Diagram  for  Panel  under 
Engine  Load. 


beams,  the  amount  transferred  to  Lt  will 
be  the  reaction  of  the  stringer  LtL2.  Re- 
ferring to  Fig.  89,  the  reaction  is: 

RLi  =  (20  X  9  +  20  X  14  +  20  X  19)   -   20 
=  42.0 

The  shear  in  the  second  panel  is  now 
found  to  be: 

F2  =  143.6  -(10  +  20  +  42.0)  =  +71.6 
In  the  majority  of  cases  where  it  is 
necessary  to  determine  the  shear  in  a 
panel,  none  of  the  loads  will  be  in  the 
panel  to  fhe  left  of  the  one  under  consid- 
eration. In  this  case  the  operation  is 
somewhat  simplified,  as  the  engine  dia- 
gram can  be  used  directly.  If  the  engine 
be  placed  so  that  the  third  wheel  is  at 
L2,  wheel  16  will  be  just  over  the  right 
support,  and  the  left  reaction  will  be : 
Ri  =  12041  •*-  120  =  100.3. 

As  there  are  no  wheel  loads  in  the  first  panel,  the  amount  to  be  sub- 
tracted from  the  reaction  will  be  that  proportion  of  the  loads  1  and  2 
which  is  transferred  to  Z^  and  this  (see  Fig.  90)  is  230  -f-  20  -  11.5. 
The  shear  in  the  second  panel  is  then  100.3  -  11.5  =  +88.8. 

From  inspection  of  the  resulting  shear  in  the  second  panel  when 
wheel  6  is  at  L2  and  when  wheel  3  is  at  Z/2,  it  is  seen  that  different 
wheels  at  L2  will  give  different  shears  in  the  panel  to  the  left.  Evi- 
dently there  is  some  wheel  which  will  give  the  greatest  shear  possible. 
The  same  is  true  of  the  relation  between  wheels  and  moments-  The 


88 


BRIDGE  ENGINEERING 


79 


next  two  articles  are  devoted  to  subject-matter  which  will  enable. one 
to  tell  which  of  several  wheels  is  the  correct  wheel  at  the  point,  without 
the  necessity  of  solving  for  the  shear  each  time  every  wheel  is  at  the 
point. 

45.  Position  of  Wheel  Loads  for  Maximum  Shear.  By  methods 
of  differential  calculus,  it  can  be  proved  that,  for  any  system,  either 
of  wheel  loads  or  wheel  loads  followed  by  a  uniform  load  (see  Fig.  91), 
the  correct  wheel  that  should  be  at  the  panel  point  6  in  order  to 


Fig.  90.    Determination  of  Shear  in  Panel  under  Engine  Load. 

give  a  very  great  or  maximum  shear  in  the  panel  a  —  b,  is  such  a 

W  W 

wheel   that   the  quantity  Q  =  -     —  G  is  positive  when  q  =  - 

(G  +  -P)  is  negative.     In  these  equations, 

W  =  Total  load  on  the  truss; 

m    =  Number  of  panels  in  the  truss; 

G    =  Load  in  panel  under  consideration;  and 

P    =  Load  at  panel  points  on  right  of  panel. 

If  a  load  is  directly  over  the  panel  point  a,  it  is  not  to  be  included  in 
the  weight  G;  neither  is  P  included  in  the  weight  G.  If  a  wheel  load 
should  come  directly  over  the  right  end  of  the  truss,  it  should  not  be 
considered  in  the  quantity  W. 

The  only  way  to  determine  which  wheel  is  the  correct  one,  is 
to  try  wheel  1,  then  wheel  2,  and  so  on,  until  the  wheel  or  wheels  are 
reached  that  will  give  the  Q  and  q  signs  of  an  opposite  character. 


89 


80 


BRIDGE  ENGINEERING 


The  process  should  not  be  stopped  there,  but  the  next  succeeding 
wheels  should  be  tried  until  Q  and  q  again  have  the  same  sign. 

As  an  example,  let  it  be  required  to  determine  the  position  of  the 
wheel  loads  to  produce  the  maximum  positive  shears  in  a  6-panel 
120-foot  Pratt  truss.  This  work  should  be  arranged  in  tabular  form, 
and  Table  V  is  found  to  be  convenient. 

TABLE  V 
Determination  of  Position  of  Wheel  Loads  for  Maximum  Shear 

(m  =  6) 


PANEL 
POINT 

WHEEL 

AT 

POINT 

<? 

w 

m 

P 

G  +  P 

Q 

ft 

REMARKS 

L, 

2 

10 

T  -  ™ 

20 

30 

+ 

•f 

292 

"\ 

3 

30 

-T  =  48-67 

20 

50 

+ 

— 

gives  a  maximum 

302 

Li 

4 

50 

^p  =  50.03 

20 

70 

+ 

— 

gives  a  maximum 

L, 

5 

00 

6 

20 

100 

'- 

-.. 

L, 

2 

10 

~-  =  38.67 

20 

30 

+ 

+ 

245 

L* 

3 

30 

nr  =  40-83 

20 

50 

+ 

— 

gives  a  maximum 

L2 

4 

50 

-^p-  =  43.00 

20 

70 

- 

- 

L3 

1 

0 

^-  -  2,07 

10 

10 

+ 

+ 

L3 

2 

10 

—  g—  =  28.67 

20 

30 

+ 

- 

gives  a  maximum 

192 

^ 

3 

30 

nr  -  34-° 

20 

50 

+ 

- 

gives  a  maximum 

L3 

4 

50 

—^   =  37.0 

20 

70 

- 

- 

L, 

1 

0 

=  19.33 

10 

10 

+ 

+ 

L4 

2 

10 

^~  =  21.50 

20 

30 

4- 

- 

gives  a  maximum 

L< 

3 

30 

-4—  =  23.67 
b 

20 

50 

- 

- 

Ls 

1 

0 

T-  -  n'67 

10 

10 

+ 

+ 

L5 

2 

10 

f-   =  15.00 

20 

30 

+ 

- 

gives  a  maximum 

L& 

3 

30 

~   =  17.17 

20 

50 

- 

- 

90 


o  •< 

OS     S 

J  ! 


i! 
|1 
si 


BRIDGE  ENGINEERING 


A  study  of  Table  V  shows  the  fact 
that  wheel  1  can  never  produce  a  maxi- 
mum. It  also  shows  that  there  are  in 
some  cases  two  positions  which  will  give 
large  values  of  the  moment.  In  these 
cases  the  shears  for  each  position  of  the 
engines  must  be  determined  in  order  to 
tell  which  wheel  at  the  panel  point  in 
reality  gives  the  greatest.  In  practical 
work  it  is  customary  to  use  the  first 
position  found,  as  the  difference  in  the 
shears  resulting  from  the  use  of  the  two 
positions  is  not  large  enough  to  affect  the 
final  design. 

Fig.  92  shows  the  engine  diagram 
on  the  truss  in  the  correct  position  to 
give  the  maximum  shear  in  the  second 
panel.  The  weight  of  wheel  16  is  not 
included  in  the  weight  W,  as  it  is  directly 
over  the  right  support. 

46.  Position  of  Wheel  Loads  for 
Maximum  Moments.  In  this  case  the 
methods  of  differential  calculus  are  em- 
ployed to  determine  which  wheels  will,  if 
placed  at  a  point,  give  a  maximum  mo- 
ment at  that  point.  For  any  system, 
either  of  wheel  loads  or  of  wheel  loads 
followed  by  a  uniform  load,  that  wheel 
Wn 


which  will   cause    K 


—      —  L  to  be  positive,  and  k  = 
m  m 


(L  +  P)  to  be  negative,  is  the  wheel.  Here  n  is  the  number  of  the 
panel  under  consideration,  and  is  to  be  reckoned  from  the  left 
end;  L  =  the  load  to  the  left  of  the  point  under  consideration; 
and  the  remainder  of  the  letters  signify  the  same  as  they  do  in 
Article  45.  In  some  cases  there  will  be  more  than  one  position 
of  the  loads  which  will  satisfy  the  above  condition.  It  is  then 
necessary  to  work  out  the  actual  moments  created  by  the  loads 
in  each  position,  in  order  to  find  out  which  is  the  largest.  The 


91 


g2 


BRIDGE  ENGINEERING 


position  of  the  loads 
for  the  greatest  mo- 
ments should  be  de- 
termined for  all  panel 
points  except  the  one 
on  the  extreme  right, 
as  the  greatest  moment 
possible  maybe  caused 
by  wheels  of  the  rear 
engine  being  on  the 
point  on  the  right- 
hand  side  of  the  truss, 
instead  of  the  wheels 
of  the  front  engine  be- 
ing at  the  correspond- 
ing point  on  the  left- 
hand  side. 

In  general,  it  may 
be  said  that  there  will 
be  a  number  of  wheels 
which,  if  placed  at  the 
panel  point  in  the  cen- 
ter of  the  span,  will 
satisfy  the  given  con- 
ditions. In  this  par- 
ticular case,  it  is  not 
necessary  to  determine 
all  of  the  moments. 
The  greatest  moment 
possible  will  occur 
when  that  one  of  the 
heaviest  wheels  of  the 
second  locomotive 
which  gives  the  heav- 
iest load  upon  the 
truss  is  at  the  point. 
In  case  several  of  the 
heavy  wheels  give  the 


BRIDGE  ENGINEERING 


83 


same  maximum  load  W,  use  the  first  wheel  which  gives  this  max- 
imum W. 

Let  it  be  required  to  determine  the  position  of  the  wheel  loads 
for  maximum  moments  at  the  lower  panel  points  of  the  6-panel  120- 
foot  Pratt  truss  of  Article  45.  The  necessary  work  can  be  con- 
veniently arranged  in  the  form  of  a  table,  as  is  done  in  Table  VI. 

TABLE  VI 
Determination  of  Position  of  Wheel  Loads  for  Maximum  Moments 


PlNEL 

WHEEL 

Wn 

POINT 

AT 

POINT 

L 

P 

L  +  r 

K 

k 

REMARKS 

£, 

2 

10 

284  -=-  6  =  47.3 

20 

30 

+ 

+ 

LI 

3 

30 

292  -s-  6  =  48.7 

20 

50 

+ 

— 

gives  a  maximum 

L, 

4 

50 

302  -=-  6  =  50.3 

20 

70 

+ 

— 

gives  a  maximum 

LI 

5 

60 

302  -s-  6  =  50.3 

20 

80 

- 

— 

wheel  1  is  off  bridge 

La 

5 

70 

(271^6)X2=    90.3 

20 

90 

+ 

+ 

L3 

6 

90 

(290n-6)X2=    96.7 

13 

103 

+ 

gives  a  maximum 

L2 

7 

103 

(300  -5-6)  X2=  100.0 

13 

116 

- 

L3 

8 

116 

(271  -5-6)  X3  =  135.5 

13 

129 

+ 

+ 

L3 

9 

129 

(284-6)X3  =  142.0 

13 

142 

+ 

gives  a  maximum 

L3 

10 

142 

(298^6)  X3=  149.0 

10 

152 

+ 

— 

sjives  a  maximum 

L3 

11 

142 

(304  -h  6)  X  3  =  15  1.3 

20 

162 

+ 

_ 

gives  a  maximum 

1L3 

12 

142 

(294-6)X3  =  147.0 

20 

162 

+ 

_ 

gives  a  maximum 

L, 

13 

142 

(284  H-  6)  X3=  142.0 

20 

162 

0 

_ 

gives  a  maximum 

L3 

14 

142 

(274  -5-6)  X3=  137.0 

20 

162 

— 

- 

L< 

11 

152 

(271  -5-  6)  X4  =  180.6 

20 

162 

•f 

+ 

Note  wheel  18  not 

included. 

L< 

12 

172 

(284n-6)X4=189.4 

20 

192 

+ 

— 

gives  a  maximum 

L< 

13 

192 

(294-h6)X4=196.0 

20 

212 

+ 



gives  a  maximum 

L\ 

14 

212 

(304  --  6)  X4  =  202.  6 

20 

232 

- 

One  should  carefully  note  that  in  certain  positions,  as  when 
wheels  11,  12,  13,  and  14  are  at  L#  some  wheels  are  to  the  left  of  the 
left  support;  that  is,  they  are  not  upon  the  bridge.  In  all  such  cases 
they  are  counted  neither  in  the  quantity  L  nor  in  W, 

In  the  case  of  Z/3,  wrheel  11,  being  the  first  large  driver  of  the 
second  engine,  wrill  give  the  greatest  moment,  as  it  is  the  first  driver 
to  come  at  the  point  when  the  maximum  load  of  304  000  pounds  is  on 
the  truss.  Fig.  93  shows  the  engine  diagram  on  the  truss  in  correct 
position  to  give  the  maximum  moment  at  point  Lr 

47.  Pratt  Truss  under  Engine  Loads.  In  order  to  exemplify 
the  use  of  the  engine-load  diagram,  let  it  be  required  to  determine  the 
stresses  in  the  Pratt  truss  of  Article  45  due  to  E  40  loading,  the 


93 


84 


BRIDGE  ENGINEERING 


height  being  25  feet.  The 
secant  is  (~2?  +  20*)*  -=-25  = 
1.28. 

The  maximum  positive 
shears  in  the  various  panels 
should  first  be  computed. 
These,  written  in  reverse  or- 
der, will  be  the  maximum 
negative  or  minimum  shears. 
Table  V  should  now  be  re- 
ferred to,  and  an  outline  dia- 
gram drawn  to  the  same  scale 
as  the  engine  used,  on  which 
to  place  the  engine  diagram  in 
the  correct  position.  The  vari- 
ous values  can  then  be  read 
off  the  diagram  at  the  right- 
hand  end  of  the  truss.  It  will 
be  found  convenient  to  lay  off 
to  scale  the  first  ten  feet  of 
the  lower  chord  of  the  truss 
from  the  right  support,  mak- 
ing the  divisions  one  foot  apart. 
This  will  enable  one  to  ascer- 
tain the  distance  of  the  last 
wheel  load  from  the  right  sup- 
port, or  the  amount  of  uni- 
form load  upon  the  bridge, 
without  scaling  or  further  com- 
putation. In  case  it  is  desired 
to  have  the  wheel  loads  appear 
on  the  lower  chord,  as  in  Fig. 
93,  the  outline  of  the  truss 
should  be  on  tracing  cloth  or 
transparent  paper.  This  is  not 
to  be  advised,  however,  as  er- 
rors are  likely  to  occur  because 
of  failure  to  distinguish  clearly 


BRIDGE  ENGINEERING  85 

the  various  numerical  values.  It  is  far  better  to  place  the  diagram 
as  in  Fig.  92,  in  which  case  the  outline  of  both  the  truss  and  the  dia- 
gram can  be  drawn  on  good  stiff  paper. 

For  wheel  3  at  point  Ll  (see  Articles  44  and  45),  the  left  reaction 
is  as  follows,  there  being  four  feet  of  uniform  load  upon  the  truss: 

Ri   =    ( 16  364  +  284  X  4  +    4*  *  2'°)  -h  120  =  146.0; 

and  the  proportion  of  loads  in  the  panel  which  is  transferred  to 
the  point  L0  by  the  stringers  is  230  4-  20  =  11.5.  The  shear  is 
therefore  F,  =  +146.0  -  11.5  =  +134.5.  The  computation  for 
the  shear  when  wheel  4  is  at  the  point,  will  not  be  made;  for,  as  has 
been  noted  before,  the  result  will  not  be  much  different  from  the 
above. 

For  wheel  3  at  L2,  wheel  16  comes  over  the  right  support.     The 
left  reaction  is: 

Ri  =  12041  +  120  =  100.3; 

the  proportional  part  of  the  loads  which  is  transferred  to  L^  is  11.5; 
and  the  shear  is: 

F2  =  (  +  100.3  -  11.5)  =   +88.8. 

For  wheel  2  at  L3,  wheel  11  comes  four  feet  from  the  right  sup- 
port.    The  left  reaction  is: 

Ri  =  (5  848  +  172  X  4)  H-  120  =  54.5. 

That  part  of  wheel  1  which  is  transferred  to  L2  is  80  -f-  20  =  4.0, 
and  the  shear  is  therefore: 

V3  =  (  +  54.5  -  4)  =   +50.5. 

For  wheel  2  at  L4,  wheel  9  comes  over  the  right  support.     The 
left  reaction  is: 

Rl  =  3  496  *  120  =  29.1. 

That  part  of  wheel  1  which  is  transferred  to  L3  is  4.0,  and  the  shear 
is  therefore: 

F4  =  (  +  29.1  -  4.0)  =   +25.1. 

For  wheel  2  at  L5,  wheel  5  is  five  feet  from  the  right  support, 
and  the  left  reaction  is: 

fli  =  (830  +  90  X  5)  -  120  =  10.7 
and  the  shear  is : 

F5  =  (  +  10.7  -  4.0)  =   +6.7. 


86  BRIDGE  ENGINEERING 

If  the  dead  panel  load  is  20  000  pounds,  all  the  shears  may  now 
be  written  as  follows: 


DEAD-LOAD  V 

4-  LIVE-LOAD  V 

-  LIVE-LOAD  V 

Vl  =    +50.0 

+  134.5 

±     0.0 

F2  =   +30.0 

+    88.8 

-     6.7 

V,  =   +  10.0 

+    50.5 

-25.1 

F4  =   -10.0 

+   25.1 

-50.5 

Vs  =   -30.0 

+      6.7 

-88.8 

F6  =   -50.0 

±     0.0 

-134.5 

A  comparison  of  the  shears  in  the  third  and  fourth  panels  shows 
that  counters  are  required.     The  stress  in  these  counters  is: 
U3L2  =  U3Lt  =   +1.28  X  (25.1  -  10.0)  =   +19.2 

As  it  is  known  that  positive  shears  cause  a  compressive  stress 
in  L0Ul  and  tensile  stresses  in  the  diagonals,  and  that  negative 
shears  produce  compressive  stresses  in  the  intermediate  posts,  the 
left  half  of  the  bridge  being  considered,  the  web  stresses  for  dead  and 
live  load  can  be  determined  without  in  all  cases  writing  the  stress 
equations  in  order  to  determine  the  sign.  It  should  be  remembered 
that  one-third  of  the  dead  panel  load,  or  6  700  pounds,  is  applied  at 
the  panel  points  of  the  top  chord. 

Dead-Load  Stresses  in  the  Diagonals  — 

L0U,  =  -1.28  X  50  =  -64.0 
U,L2  =  +1.28  X  30  =  +38.4 
U2L3  =  +1.28  X  10  =  +12.8 

Dead-Load  Stresses  in  the  Verticals.  For  U^LV  the  section 
passed  will  cut  UJJV  U^LV  and  L2L3,  and  the  shear  on  this  section 
will  be  50  -  2  X  13.3  -  6.7  =  +  16.7.  The  stress  equation  is 
+  16.7  +  U^  =  0,  from  which  U^  =  -16.7. 

The  dead-load  stress  in  U3L3  is  found  by  passing  a  circular  sec- 
tion around  U3.  Then  -  U3L3  -  6.7  =  0,  from  which  U^  =  -6.7. 
In  a  similar  manner,  by  passing  a  section  around  Lv  the  stress  is 
found  to  be  +  13.3. 

Live-Load  Stresses  in  the  Diagonals  — 

MAXIMUM  MINIMUM 

L0Ul  =   -1.28  X  134.5  =  -172.2  0 

t/jZ/2  =   +1.28  X    88.8  =  +113.6  -1.28  X  6.7  =   -8.6 

UJL3  =   +1.28  X    50.5  =  +   64.7  0 

Live-Load  Stresses  in  the  Verticals.  The  maximum  stress  in 
U1L1  occurs  when  one  of  the  large  drivers  is  at  Lv  and  the  loads  iu 


96 


BRIDGE  ENGINEERING 


87 


the  first  panel  are  as  near  as  possible  one-half  the  sum  of  the  loads 
in  panels  1  and  2  and  the  load  at  Lr  This  can  be  established  as  a 
fact  by  use  of  the  differential  calculus.  In  the  present  case,  this  con- 
dition is  satisfied  when  wheel  4  is  at  Lv  Then  the  weight  of  the 
wheels  in  panel  1  is  50  000  pounds,and  the  sum  total  is  116  000  pounds. 
If  wheel  13  be  placed  at  Lv  the  result  will  be  the  same,  and  then  the 
engine  diagram  can  be  used.  Fig.  94  represents  the  engine  diagram 
in  place,  ready  to  use.  According 
to  Article  44,  the  value  480  is  the 
moment  of  wheels  10  to  12  about 
Lr  Therefore  480  +  20  (20  is 
the  panel  length)  =  24.00,  is  that 
amount  of  wheels  10  to  12  which 
is  transferred  to  L0.  In  like 
manner,  529  -=-  20  =  26.45  is  the 
amount  of  wheels  14  to  16  trans- 
ferred to  L2.  As  the  total  weight 
of  the  loads  in  the  two  panels  is 
116000  pounds,  the  amount 
transferred  to  Ll  must  be  116.0 
-  (24.00  +  26.45)  =  65.55,  and 
the  stress  in  UlLi  is  therefore 
+  65.55. 

The  maximum  live-load  stress 
in  LJJ2  occurs  when  the  loading 
is  in  a  position  to  give  the  maxi- 
mum shear  in  the  third  panel,  as 
the  shear  at  a  section  cutting  UJJ2,  U^L^  and  L2L3  is  the  same' as 
that  at  a  vertical  section  in  the  panel.  The  stress  equation  is  +  U2La 
+  50.5  =  0,  from  which  U2L2  =  —50.5.  In  a  similar  manner,  the 
stress  equation  for  the  maximum  live-load  stress  in  U3L3  is  +  U3L3 
+  25.1  =  0,  as  UyLt  is  working,  and  therefore  U^  =  -25.1.  As  in 
the  case  of  the  analysis  of  the  Pratt  truss  under  uniform  load  (see 
Article  39),  the  dead-load  stress  of  —6.7  cannot  be  added  to  this 
stress  of  —25.1  to  obtain  the  maximum;  but  the  dead-load  stress  in 
t^  must  be  obtained  when  diagonals  UgLt  and  U^Li  are  in  action. 
In  the  manner  explained  in  Article  39,  this  is  found  to  be  +3.30. 

It  will  be  found  that  as  the'engines  come  on  the  bridge  from  the 


Fig.  94.    Engine  Diagram  for  Determina- 
tion of  Live-Load  Stress  in  Vertical 
of  Pratt  Truss. 


97 


88  BRIDGE  ENGINEERING 

left,  the  counters  come  into  action  in  the  case  of  U2L2;  and  in  the 
case  of  U3L3,  both  C72I/3  and  L3U4  act,  thus  causing  the  live-load  stress 
in  these  verticals  to  be  zero ;  and  when  this  is  the  case,  the  dead-load 
stress  is  —  6.7,  which  is  the  minimum. 

Dead-Load  Chord  Stresses.  The  dead-load  chord  stresses  can 
be  found  by  any  of  the  methods  previously  given;  but  they  will  be 
found  by  the  tangent  method  as  indicated  below,  the  tangent  being 
20  -r-  25  =  0.8: 

L0Lt  =   +0.8  X  50  =   +40.0  =  L,L2 
V*U,  =   -(50  +  30)  X  0.8  =  -  64.0 
U2U3  =   -(50  +  30  +  10)  X  0.8  =   -72.0 
L2L3  =   -U1U,=   -(-64.0)  -   +64.0 

Live-Load  Chord  Stresses.  On  account  of  the  wheel  loading,  nc 
ratio  can  be  established  between  these  stresses  and  the  dead-load 
chord  stresses.  The  maximum  moments  at  each  point  must  be 
determined,  and  these  divided  by  the  height  of  the  truss  will  give  the 
chord  stresses.  For  all  points  to  the  left  of  the  center  of  the  bridge, 
the  main  diagonal  will  act.  For  points  to  the  right  of  the  center,  an 
uncertainty  exists.  The  shear  in  the  panels  on  either  side  of  the 
point  under  consideration  should  be  determined  when  the  loading  is 
in  position  to  give  the  maximum  moment  at  that  point.  This  will 
indicate  which  diagonals  act,  which  fact  will  indicate  for  what  chord 
member  that  point  is  the  center  of  moments. 

When  wheel  3  is  at  Lv  four  feet  of  uniform  load  are  on  the  truss, 
and  the  left  reaction  is: 

Ri=  (16  364  +  384  X  4  +  — *—)  -  120  =  146.0. 

The  moment  of  this  reaction  about  Lv  less  the  moment  of  wheels  1 
and  2  about  Lv  will  be  the  moment  at  Ll  due  to  this  loading.  The 
moment  of  wheels  1  and  2  about  Ll  is  taken  from  the  diagram,  where 
it  occurs  in  the  first  line  of  values  just  to  the  right  of  the  vertical  line 
through  wheel  3,  and  therefore: 

M,  =  146.0  X  20  -  230  =  2  690  000  pound-feet. 

When  wheel  4  is  at  Lv  there  are  nine  feet  of  uniform  load  on 
the  truss,  and  the  left  reaction  is: 

A  =  (16  364  +  284  X  9  +  — ~  )  ~  120  =  158.0; 
and  in  this  case, 

M,  =  158.0  X  20  -  480  =  2  680  000  pound-feet. 


BRIDGE  ENGINEERING  89 

As  this  is  less  than  when  wheel  3  is  at  the  point,  wheel  3  gives  the 
greatest  moment. 

When  considering  the  point  L2  with  wheel  6,  the  left  reaction  is: 

Ri  =  (16  364  +  284  X  3  +  ^~)  +  120  =  143.5 
M2  =  143.5  X  2  X  20  -  1  640 
=  4  100  000  pound-feet. 

The  conditions  at  L3  indicate  that  there  are  several  wheels  which 
give  large  moments;  but  according  to  Article  46,  wheel  11  gives  the 
maximum  moment.  When  this  wheel  is  at  L3,  wheel  1  is  off  the 
truss,  and  15  feet  of  uniform  load  are  on  the  truss.  The  moment  of 

all  the  loads  about  the  right  support  is  19  304  +  304  X  5  +  5' *  2 

=  20  849,  from  which  should  be  subtracted  the  moment  of  wheel  1 
about  the  right  support.  This  moment  of  wheel  1  is  10  X  124  = 
1  240,  and  the  moment  about  L6  of  all  loads  on  the  truss  is  20  849 
-  1  240  -  19  609.  The  left  reaction  is : 

Ri  =  19  609  -f-  120  =  163.4 
M3  =  163.4  X  3  X  20  -  (5  848  -  10  X  64) 
=  4  596  000  pound-feet. 

In  the  case  of  L.,  the  reactions  and  the  moments  for  the  two 

/ 
positions  are : 

For  wheel  12,  Ri  =  16364  -s-  120=  136.4 

M4  =  136.4  X  4  X  20  -  6  708 
=  4  204  000  pound-feet. 

52  X  2 
For  wheel  13,     Ri  =  (16  364  +  5  X  284  +    — ^—)  •*-  120  =  148.4 

M4  =  148.4  X  4  X  20  -  7  668 
=  4  204  000  pound-feet, 

which  shows  that  each  wheel  gives  the  same  moment,  and  also  that 
the  moment  is  greater  than  that  at  L2,  the  corresponding  point  on  the 
left-hand  side  of  the  center  of  the  truss.  As  L2  is  the  center  of 
moments  of  UJJ2,  then,  if  the  center  of  moments  for  UJJ5  falls  at 
I/4  (that  is,  if  LJJ.  acts),  the  stress  in  UJJb  will  be  greater  than  the 
stress  in  UJJ2  when  wheel  6  is  at  L2.  Of  course,  if  the  engine  came 
on  the  truss  from  the  left,  UJJ2  would  receive  the  same  stress  that 
U4U5  now  receives.  According  to  the  shears,  LtU5  always  acts,  and 
therefore  the  center  of  moments  for  UJJ5  does  fall  at  L4. 


99 


90 


BRIDGE  ENGINEERING 


3 


LOWER  CHORD 

_? 

0    ^ 

3$ 

+    + 

(M    0 

1^ 

+    + 

J 
_f 

_f 
J 

0    1C 

§1 

+  + 

"?    9 
§5 

+    + 

O   lO 

S| 
+  + 

1C    0 
t_"   o 

+  + 

.  UPPER  CHORD 

P 
p" 

O    CO 

gg 

1    1 

X   O 

s  s 

(M 

1       1 

p" 
p" 

O    <N 

8|j 

1    1 

<M    0 

1    ^ 
1       1 

fc 
o 
o 

Q 

p_ 

,_f 

00    O    O 

<>i  o  ci 

r-t            CO 

!         + 

(M    0       ' 
05    0 

+ 

_f 
p" 

00    i-    0 

23d 
+  + 

1C    0 

j:'0' 

+ 

4 
p" 

-dH    CD    CO 

OO    CO    GO 
CO;H 

+  +  1 

o  co 

gs 

+  + 

VERTICALS 

H? 
P" 

t"»  CO  i-H  O 

coco'-cd 

oo  i- 

c^  * 

1    1 

J 
P" 

t~   1C   O 

^§6 

1    1 

<M    t-- 
t-"   CD 

CD      T-l 

1       1 

j" 
P" 

CO    CD   0 

s  s  °1 

+  + 

05    CO 

gs 

+  + 

END-POST 

P 

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sg° 

1    1 

oq  o 

CO    O 

1    1 

KIND  OF 
STRESS 

Dead-Load. 
Live-Load.. 

Maximum.. 
Minimum.  . 

The  various  moments  are  written 
in  order,  as  such  action  will  facili- 
tate the  remainder  of  the  computa- 
tions. 

Af ,  =  2  690 

M2  =  4  100 

M\  =  4  596 

M4  =  4  204 

The  chord  stresses  are  now  found 
to  be: 


L0L,  =  L,  L2  =  + 


U,Ut  =  - 


2690 

25 
4  100 


107.5 


=    -  164.0 


Ifi        -183.3 
lfi=-168. 


L,L3  =  -  U,L2  =  -  (  -  164.2)  =  +  164.2 
L3L4  =  -UtUs=  -(-  168.2)  =  +  168.2 

When  the  load  comes  on  from  the 
left,  the  stresses  in  UtU2  and  L2L3 
will  be  -168.2  and  +168.2  respec- 
tively, which  are  the  maximum  live- 
load  stresses  for  these  members. 

Instead  of  placing  the  values  of 
the  stresses  on  a  truss  outline,  they 
are  sometimes  put  in  tabular  form, 
as  in  Table  VII. 

48.  Impact  Stresses.  When  an 
engine  is  at  rest  on  a  bridge,  the 
stresses  in  the  members  are  the 
same  as  those  computed  for  that 
loading.  When  the  loads  move 
across  the  bridge  at  any  speed,  the 
vibrations  and  the  shocks  produced 
by  the  counterweights  in  the  drivers 
and  by  other  causes  create  stresses 
in  the  various  members  in  excess 
of  those  computed  by  aid  of  the 
engine  diagram.  The  excess  stresses 


ICC 


BRIDGE  ENGINEERING  91 


are  designated  as  impact  stresses.  This  term,  however,  is  mislead- 
ing to  a  certain  extent,  as  causes  other  than  the  impact  or  pounding 
of  the  engine  wheels  help  to  produce  the  stresses  referred  to. 

It  is  a  well-known  fact  capable  of  mathematical  demonstration, 
that  a  load,  if  suddenly  applied,  will  produce  a  stress  equal  to  twice 
that  which  it  will  produce  as  a  static  load;  also,  that  as  the  ratio  of 
the  weight  of  the  load  to  the  weight  of  the  structure  increases,  the 
vibrations  produced  by  the  impact  will  be  less.  These  two  facts  are 
the  basis  of  most  of  the  empirical  formulae  for  impact  stresses;  and 
empirical  formulae  are  used  to  obtain  these  stresses,  as  the  existing 
conditions  and  producing  causes  are  not  such  as  to  make  them  sus- 
ceptible of  mathematical  treatment.  The  result  of  experiments 
on  actual  bridges  under  the  effect  of  passing  engines  and  trains,  have 
been  the  basis  of  many  formulae.  One  of  these  is : 

300 


L  +  300' 


where  /  =  Impact  stress  in  the  member; 

S  =  Live-load  stress  in  the   member   caused   by  the  engine 

load  when  at  rest ; 
L  =  Length  of  that  part  of  the  bridge  which  is  loaded  when 

the  stress  S  is  produced;  and 
300  =  A  constant. value  derived  from  experiments. 

This  formula  was  proposed  by  C.  C.  Schneider  in  1887,  and  is 
given  in  the  "Transactions"  of  the  American  Society  of  Civil  En- 
gineers, Vol.  34,  page  331.  While  it  does  not  take  into  considera- 
tion the  relative  weights  of  the  bridge  and  the  live-load  loads,  this 
formula  does  make  allowance  for  the  time  it  takes  to  produce  the 
stress,  by  introducing  L,  the  distance  over  which  the  engine  passes 
before  causing  the  stress  S.  It  is  seen  that  the  smaller  the  distance  L, 
the  greater  will  be  the  impact  stress  for  any  given  value  of  S.  When 
L  becomes  exceedingly  small,  the  effect  would  be  that  of  a  suddenly 
applied  load,  and  the  impact  stress  would  equal  the  stress  S.  Table 

300 

VIII  gives  the  values  of  T .,„„  ,  which    is    called    the  impact  co- 

Li  T  oOU 

efficient,  for  different  values  of  L.     Values  not  given  may  be  inter- 
polated. 

For  example,  by  consulting  Fig.  92,  which  gives  the  position  of 
the  engines  for  the  maximum  live-load  stress  in  UJjv  it  is  seen  that 
93  feet  (the  distance  from' wheel  1  to  the  right  support)  is  the  loaded 


lol 


92 


BRIDGE  ENGINEERING 


ITABLE  VIII 
Values  of  the  Impact  Coefficient 


L 

300 

L 

300 

L  +  300 

L 

300 
L  +  300 

L 

300 
L  +  300 

L 

300 
L  +  300 

L  +  300 

5 
6 
7 
8 
9 
10 

11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

0.984 
0.980 
0.977 
0.974 
0.971 
0.968 

31 

32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

0.906 
0.904 
0.901 

0.898 
0.896 
0.893 
0.890 

0.888 
0.885 
0.882 

57 
58 
59 
60 

0.840 
0.838 
0.836 
0.833 

83 

84 
85 
86 
87 
88 
89 
90 

91 
92 
93 
94 
95 
96 
97 
98 
99 
100 

0.783 
0.781 
0.779 
0.777 
0.775 
0.773 
0.771 
0.769 

145 
150 

0.674 
0.667 

155 
160 
165 
170 
175 
180 
185 
190 
195 
200 

210 
220 
230 
240 
250 
260 
270 
280 
290 
300 

0.659 
0.652 
0.645 
0.638 
0.632 
0.625 
0.619 
0.612 
0.606 
0.600 

61 
62 
63 
64 
65 
66 
67 
68 
69 
70 

0.831 
0.829 
0.826 
0.824 
0.822 
0.820 
0.817 
0.815 
0.813 
0.811 

0.965 
0.962 
0.958 
0.955 
0.952 
0.949 
0.946 
0.943 
0.940 
0.937 

0.767 
0.765 
0.763 
0.761 
0.759 
0.758 
0.756 
0.754 
0.752 
0.750 

0.880 
0.877 
0.875 
0.872 
0.870 
0.867 
0.865 
0.862 
0.860 
0.857 

0.588 
0.577 
0.566 
0.556 
0.546 
0  .  536 
0.526 
0.517 
0.508 
0.500 

71 

72 
73 
74 
75 

76 

77 
78 
79 
80 

0.809 
0.806 
0.804 
0.802 
0.800 
0.798 
0.796 
0.794 
0.792 
0.789 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

0.935 
0.932 
0.929 
0.926 
0.923 
0.920 
0.917 
0.915 
0.912  1 
0.909 

105 
110 
115 
120 
125 
130 
135 
140 

0.741 
0.732 
0.725 
0.714 
0.706 
0.698 
0.690 
0.682 

51 
52 
53 
54 
55 
56 

0.855 
0.852 
0.850 
0.847 
0.845 
0.843 

400 
500 
600 

0.429 
0.375 
0.333 

81 
82 

0.787 
0.785 

length.  From  Table  VII,  it  is  seen  that  the  stress  in  C7,L2  produced 
by  this  loading  is  + 118.6;  and  from  Table  VIII,  the  impact  coefficient 
for  93  feet  is  found  to  be  0.763.  The  impact  stress  is  now  computed : 

/  =  0.763  X  118.6  =   +90.6. 
The  maximum  stress  in  UtL2  is  now : 

Dead-load  =  +  38.4 
Live-load  =  +118.6 
Impact  =  +  90.6 


Maximum  =   +247.6 


Table  IX  gives  the  necessary  information  for  computing  the 
impact  stresses,  and  also  gives  the  impact  stresses  corresponding  to 
the  maximum  live-load  stresses  in  the  members  of  the  truss  of  Article 
47. 


102 


BRIDGE  ENGINEERING 


93 


TABLE  IX 
Impact  Stresses  in  a  Pratt  Truss 


MEMBER 

s 

L 

300 

/ 

RKMARKS 

L+  300 

L0U, 

-172.2 

113 

0.727 

-125.2 

4  ft.  of  uniform  load  on  truss 

C7,L, 
U2L2 
U3L3 

+    65.6 
-   50.5 
-   25.1 

37 

68 

48 

0.890 
0.815 
0.862 

+    58.4 
-    41.3 
-    21.6 

See  succeeding  text. 
Same  as  for  U2L3 
Same  as  for  C/3L4 

U,L2 
U2L3 

tfR 

+  118.6 
+   64.7 
+    32.0 

93 

68 
48 

0.763 
0.815 
0.862 

+    90.6 
+    52.7 
+    27.6 

Wheel  16  at  Lr> 
Wheel  11  is  4  ft.  from  L8 
Wheel  9  at  L0. 

U,U2 

utu, 

-168.2 
-183.8 

114 
114 

0.724 
0.724 

-121.8 
-133.2 

j  Wheel  13  at  L4. 
/  5  ft.  of  uniform  load  on  bridge. 
/  15  ft.  of  uniform  load  on  bridge. 
\  Wheel  1  off  bridge. 

LA 

L2L3 

+  107.5 
+  168.2 

113 
114 

0.727 
0.724 

+    78.2 
+  121.8 

Same  loading  as  for  L0Ul 
Same  loading  as  for  UyU3 

In  the  case  of  U^,  it  should  be  noted  that  only  the  wheels  10  to 
16  inclusive  cause  the  stress  (see  Fig.  94),  and  that  the  loaded 
length  is  the  distance  from  wheel  10  to  wheel  16. 

Some  specifications  do  not  call  for  impact  stresses.  The  unit- 
stresses  in  these  specifications  are  made  low,  and  the  sections  designed 
are  large  enough  to  withstand  the  additional  stresses  due  to  impact. 
In  cases  where  the  impact  stresses  are  required,  they  must  be  con- 
sidered in  computing  the  maximum  and  minimum  stresses. 

49.  Snow=Load  Stresses.  In  some  localities  the  snowfall  is 
considerable,  and  its  weight  should  be  taken  into  account  in  com- 
puting stresses.  This  should  be  done  by  considering  it  as  an  addi- 
tional dead  load  of  15  pounds  per  square  foot  of  floor  surface  for  every 
foot  of  snowfall.  As  it  covers  the. entire  floor  surface,  the  stresses 
will  be  proportional  to  the  dead-load  stresses.  Also  it  is  evident  that 
the  snow  load  should  not  be  taken  into  account  in  railroad  bridges 
unless  they  have  solid  floors,  as  most  of  it  falls  through  the  open 
spaces  between  ties  and  stringers. 

As  an  example,  let  it  be  required  to  determine  the  snow-load 
stresses  in  a  member  of  a  highway  bridge,  the  dead-load  stress  in  the 
member  being  +84.0,  the  dead  panel  load  being  12  000  pounds,  and 


103 


94  BRIDGE  ENGINEERING 

the  snow  bemg  l\  feet  deep  on  the  roadway,  which  is  14  feet  wide. 
The  snow  panel  load  is: 

-  (14  X  15  X  1£  X  20)  =  3  150  pounds. 

In  the  above  equation,  14  is  the  width  of  roadway;  15  is  the  weight 
in  pounds  of  one  square  foot  of  snow  one  foot  deep;  and  20  is  the 
length  of  one  panel.  One-half  of  the  weight  of  snow  must  be  taken, 
as  half  is  carried  b  each  truss.  The  snow-load  stress  is  then: 


In  like  manner,  all  snow-load  stresses  can  be  computed. 

Most  of  the  standard  specifications  which  have  been  published 
do  not  specify  snow  loads;  and  in  fact  it  is  not  customary  to  include 
the  snow  load  in  any  designs  except  those  for  bridges  in  extreme 
northern  latitudes.  It  is  hardly  probable  that  the  greatest  load  will 
come  upon  a  country  bridge  when  it  is  covered  with  snow.  Also, 
in  cities,  the  sidewalks  are  cleaned  of  snow;  and  so  is  the  roadway 
if  the  city  is  of  large  size. 

WIND=LOAD  EFFECTS 

50.  Top  Lateral  System  Through=Bridges.  The  unit-loads  for 
this  system  are  given  in  Article  26.  Common  practice  is  to  take 
150  pounds  per  linear  foot  of  top  chord,  the  end-post  being  con- 
sidered part  of  the  top  chord  in  this  computation. 

In  many  of  the  longer-span  modern  bridges,  the  diagonals  of 
this  system  are  designed  to  take  either  tension  or  compression  ;  but  in 
the  majority  of  the  shorter  spans,  200  feet  and  under,  while  generally 
consisting  of  angles  or  other  stiff  shapes,  they  are  designed  to  take 
tension  only.  The  verticals  or  top  lateral  struts  take  compression. 
This  combination  of  tension  diagonals  and  compression  verticals 
makes  the  so-called  Pratt  system  of  webbing;  and  indeed  the  lateral 
systems,  both  top  and  bottom,  are  Pratt  trusses  in  a  horizontal  posi- 
tion. Fig.  95  shows  the  side  elevation  of  the  truss  of  Article  47,  and 
also  the  top  and  bottom  laterals.  The  diagonals  shown  in  full  lines 
act  when  the  wind  is  right,  and  those  shown  by  dotted  lines  act 
when  the  wind  is  left.  Wind  right  indicates  that  the  wind  is  blow- 
ing from  the  right  hand  when  a  person  stands  facing  the  righ'  end  of 


104 


96 


BRIDGE  ENGINEERING 


the  bridge.  Wind  left  indicates  that 
the  wind  blows  from  a  person's  left 
when  standing  as  above  described. 

The  wind  load  of  150  pounds  is  di- 
vided between  the  two  trusses,  this 
being  exact  enough  for  practical  pur- 
poses; for,  by  actual  experiment,  the 
difference  between  the  readings  of 
wind-pressure  gauges  placed  at  points 
opposite  each  other  in  the  top  chords 
of  a  through-bridge  was  only  from  8  to 
10  per  cent. 

The  problem,  then,  is  one  of  a  deck 
Pratt  truss  with  a  dead  panel  load  of 
150  X  20  =  3.0  divided  between  the 
two  chords.  Fig.  96  shows  the  distri- 
bution of  loads  and  the  reaction,  it 
being  considered  that  the  portal  brac- 
ings and  the  end -posts  (see  Fig.  95) 
are  stiff  enough  to  distribute  the 
reaction  equally  between  the  bearing 
points  L0,  L0',  L6,  L9'.  Each  panel 
load  is  indicated  by  an  arrow,  and 
is  equal  to  3.0  ^  2  =  1.5.  The  re- 
action at  each  of  the  points  L0,  L/, 
L0,  and  LG'  is  10  X  1.5  +  4  =  3.75. 
The  truss  being  symmetrical,  the 
stresses  in  like  members  on  each  side 
of  the  center  will  be  the  same.  The 
shears  in  the  top  system  are: 

V1  ==  +2  X  3.75  -  2  X  1.5  =  +4.5 
ya-a  =  +2  X  3.75  -  3  X  1.5  =  +3.0 
V2  =  +2  X  3.75  -  4  X  1.5  =  +1.5 

and  the  secant  ^  is  (172  +  202  )*  -=-  17 
=  1.544.  The  stresses  in  the  diag- 
onals are: 

U1'U2  =   +1.544  X  4.5  =   +6.95 
U2'UZ  =   +1.544  X  1.5  =   +2.32. 


106 


BRIDGE  ENGINEERING 


97 


The  vertical  U2'U2  =  —3.0;  and  by  passing  a  section  6  —  6  around 
U9f,  the  stress  in  U3'U3  is  found  to  be  — 1.5. 

In  obtaining  the  chord  stresses  in  this  system,  the  case  is  the 
same  as  if  the  reactions  were  applied  at  U^  and  Ubr,  as  the  portal  and 
end-posts  are  not  in  the  same  plane  as  the  lateral  system.  The  tan- 
gent method  is  the  simplest  to  use  in  this  case.  The  tangent  is 
20  -f-  17  -  1.176,  and  the  stresses  (see  Fig.  95)  are: 

ff/CY  =   -  4.5  X  1.176  =   -5.29 

U*'  U3r  =   -(4.5  +  1.5)  X  1.176  =   -7.06 

17,17,     A  0 

U2U3     =   -USU,'  =   +5.29 

Fig.  97  is  a  diagram  with  the  stresses  caused  by  wind  right  and 


ul 


W.R.-   529 
W.L.+    0 


W.R.-7.06 
W.L.+  5E9 


v 


U, 


Ue 


W.R.*  0 
Fig.  97.    Wind  Stress  Diagram  of  Pratt  Truss  of  Fig.  95. 


W.R.+  5£9 
W.L.  -  7.O6 


wind  left  indicated  thereon.     The  stresses  for  wind  left  can  easily 
be  written  by  inspection. 

51.  Bottom  Lateral  Bracing,  Through=Bridges.  Fig.  95  shows 
the  lower  lateral  system  with  the  panel  points  loaded  with  the  fixed 
or  dead  wind  load.  In  this  case  it  is  all  taken  as  acting  on  one  side, 
it  being  assumed  that  the  floor  system  protects  the  leeward  truss. 
The  problem  then  becomes  that  of  determining  the  stresses  in  a  deck 
Pratt  truss  of  6  panels  of  20  feet  each,  the  height  being  1 7  feet.  When 
wind  is  right,  the  members  shown  by  broken  lines  in  Fig.  95  do  not  act. 

The  fixed  wind  load  (Article  26)  is  150  pounds  per  linear  foot  of 
chord.  The  panel  load  will  be  the  same  as  before,  3.0,  but  all  will 
be  on  one  chord.  The  shears  are: 

Vl     =  2J  X  3.0  =   +7.5 

Fa-a    =     +7.5 

F2     =   +7.5  -  3.0  =   +4.5 

Fb-b  =   +4.5 

F3     =  +7.5  -  2  X  3.0  =   +1.5 


107 


98  BRIDGE  ENGINEERING 

The  secant  being  1.544,  as  previously  computed,  the  web 
stresses  are: 

L0'L,  =  +7.5  X  1.544  =  +11.60  L/L,  =  -7.5 
L/L.,  =  +4.5  X  1.544  =  +  6.95  L/L,  =  -4.5 
L2'L3  =  +1.5  X  1-544  =  +  2.32  L/L,  =  -3.0 

The  stress  in  L3'L3  is  determined  by  passing  section  c  —  c  and 
resolving  the  vertical  forces  at  L3f  (see  Fig.  95). 

By  using  the  tangent  method,  the  chord  stresses  are  computed 
as  follows: 

L0'L,'  =   -7.5  X  1.176  =   -8.82 

L/L/  =   -(7.5  +  4.5)  X  1.176  =   -14.12" 

L,'L3'  =   -(7.5  +  4.5  +  1.5)  X  1.176  =   -15.88 

L,L2  .     -L0'L/  =   -(-8.82)  =   +8.82 

L,L3  =     -  W  =   -(-14.12)  =   +14.12 

The  wind  load  acting  on  the  train  is  450  pounds  per  linear  foot. 
It  is  evident  that  the  train  may  cover  the  span  either  partially  or 
entirely,  and  therefore  its  action  on  the  lower  lateral  system  is  the 
same  as  if  it  were  stressed  by  a  live  load  of  450  pounds  per  linear  foot 
of  truss. 

The  live  panel  load  is  450  X  20  =  9.0.  The  maximum  live- 
load  reaction  is  5  X  9.0  •+•  2  =  22.5,  and  the  positive  live-load  shears 
are: 

Vl  =   +22.5 

q  A 
F,  =  (1  +  2  +  3  +  4)  ^  =   + 15.0 

Q  O 

V,=   (1+2  +  3)^  =   +9.0 

It  is  unnecessary  to  go  further  than  the  center,  as  only  the  maximum 
stresses  are  required  in  the  members:  The  web  stresses  are  com- 
puted as  given  below : 

L0'L,  =  +22.5  X  1.544  =  +34.75  L/L,  =  -22.5 
L/L2  =  +15.0  X  1.544  =  +23.15  L/L2  =  -15.0 
L2'L3  =  +  9.0  X  1.544  =  +13.91  L3'L3  =  -  9.0 

The  maximum  chord  stresses  due  to  this  load  of  450  pounds  per 
linear  foot  of  train,  occur  when  the  train  covers  the  entire  span;  and 
they  are  directly  proportional  to  the  stresses  produced  by  the  fixed 
load,  in  the  same  ratio  as  the  live  panel  load  is  to  the  fixed  panel  load. 

9  0 

This  ratio  is  ^-  =  3.0.     The  chord  stresses,  therefore,  are: 
o.U 


108 


BRIDGE  ENGINEERING 


99 


L/L  '  = 

-    8.82 

x 

3  = 

Z-/Q  *^\ 

-26.46 

"               »^    -~^ 

L/L/  = 

-14.12 

X 

0      

+ 

-42.36 

/  \                 ~*~~ 

L/L3'  = 

-15.88 

X 

3  = 

\\           £ 

-47.64 

/\ 

L,La     = 
+  26.46 

+   8.82 

X 

3  —                                             •»      "| 

L2L3     - 

+  14.12 

X 

3   =                                                               /^o 

+  42.36 

Table  X,  Article  53, 
gives  the  stresses  in  the 
top  and  bottom  lateral 
systems  for  wind  right 
and  wind  left. 

52.  Overturning  Ef= 
feet  of  Wind  on  Truss. 
When  the  wind  blows  on 
the  top  chord,  it  tends  to 
overturn  the  truss.  As 
the  truss  is  held  down  by 
its  own  weight,  the  action 
of  the  wind  does  not 
overturn  it,  but  causes 
the  dead-load  reaction  on 
the  windward  side  to  be 
less  and  that  on  the  lee- 
ward side  to  increase  by 
a  like  amount.  The 


amount  is  ±  V  =  -^-  X 
=  the  sum 


-=-  ,  where 
b 


of  all  .the  wind  panel 
loads,  h  =  the  height  of 
the  truss,  and  b  =  the 
distance  center  to  center 
of.  trusses.  The  effect 
upon  the  leeward  truss  is 
the  same  as  if  two  ver- 


109 


100 


BRIDGE  ENGINEERING 


tical  loads,  each  equal  to  V  and  acting  downward,  were  placed  at  the 
hips  Ul  and  U5  (see  Fig.  98).  The  effect  on  the  windward  truss  is 
the  same  as  if  two  vertical  loads,  each  equal  to  V  and  acting  upward, 
were  placed  at  the  hips  C//  and  U6f. 

The  stresses  in  the  leeward  truss  will  now  be  worked  out.     The 
stresses  in  the  windward  truss  are  the  same,  but  with  opposite  signs. 

10  X  1.5        25 
2        X    17 


The  truss  is  that  of  Article  47.     Here  V 


=  11  000. 


Fig.  99  shows  the  truss  with  the  loads  in  the  correct  position,  the 


Fig.  99.    Truss  under  Wind  Loads. 

reactions  each  being  11.00.  V1  =  +11.00,  and  V2  =  +  11.00- 
11.00  =  0.  The  shears  in  the  2d,  3d,  4th,  and  5th  panels  are  also 
zero.  As  the  shear  in  these  panels  is  zero,  the  stress  in  the  diagonals 
and  vertical  posts  is  zero  X  secant  $  =  zero.  The  stress  in  the  hip 
verticals  U^  and  UbL.  is  zero,  as  there  are  no  loads  at  Lt  and  Ly 
The  stress  in  the  end-post  is  -11.00  X  1.28  -  -14.08.  Taking 
the  center  of  moments  at  TJV  the  stress  equation  of  LJL^  =  LJL2  is: 
-1^2  X  25  +  11.00  X  20  -  0;  whence  LtL2  =  +8.8.  The  stress 
in  all  the  lower  chord  members  will  be  found  to  be  +  8.8.  By 
summing  the  horizontal  forces  at  the  section  a  —  a,  noting  that,  as 
UjL2  is  zero,  its  component  is  also  zero,  there  results:  +L^L2  +  UJJ^ 
=  0;  whence  UtU2  =  -itL2  -  -  (  +  8.80)  =  -8.80.  This  is  also 
the  stress  in  all  members  of  the  top  chord. 

It  is  now  seen  that  the  overturning  effect  of  the  wind  on  the 
truss  causes  stresses  only  in  the  end-posts  and  chords.  The  wind  on 
the  lower  chord  causes  no  overturning  effect,  as  it  is  transferred 
directly  to  the  abutments. 

53.  Overturning  Effect  of  Wind  on  Train.  The  wind  blowing 
upon  the  train  tends  to  overturn  it,  and  in  so  doing  the  pressure  on 


110 


BRIDGE  ENGINEERING 


101 


the  leeward  stringer  is  increased  and  that  on  the  windward  stringer 
decreased  by  the  same  amount.  This  difference  in  pressures  is 
transferred  to  the  floor-beam  and  then  to  the  panel  points  (see  Fig. 
100),  where  its  value  is: 


±  L  = 


W  X  (8.5  +  a) 


where 


=  Panel  load  due  to  wind 

on  train; 

8.5=  A  constant  established 
by  the  Specifications 
(see  Article  26,  p.  15); 
a  =  Distance  from  base  of 
rail  to  center  line  of 
lower  chord.  It  may 
be  taken  as  3  feet  in 
most  cases,  as  this  is 
approximately  the 
usual  depth  of  floor). 
b  =  Distance  center  to  cen- 
ter of  trusses. 

'For  the  case  in  hand,  W  =  20 
X  450  =  9  000.     Therefore, 

9  000  X  (8.5  +  3) 


L  =    ± 


17 


Illustrating  Overturning  Effect  of 
Wind  on  Train. 


=  ±  6  090  pounds. 


The  action  of  the  wind  in  tending  to  overturn  the  train  is  the 
same  as  if  the  truss  were  under  a  live  panel  loading  of  L,  the  panel 
load  L  acting  upward  on  the  windward  and  downward  on  the  leeward 
truss. 

The  chord  stresses  due  to  this  will  be  proportional  to  the  dead- 
load  stresses  in  the  same  ratio  as  this  panel  load  L  is  to  the  dead  panel 


load. 


For  the  truss  of  Article  47,  this  ratio  is  ^  =  0.303,  and 

^U  UUU 


the  chord  stresses  caused  by  the  overturning  effect  of  the  wind  on  the 
train  (see  Table  VII)  are: 

tf,C72  =   -64.0  X  0.303  =   -19.39 
U2U3  =   -72.0  X  0.303  =   -21.82 
L0L,    =  L,L2  =  +40.0  X  0.303  =   +12.12 
L2L3    =   +64.0  X  0.303  =   +19.39 

The  stress  in  f/,L,  is  +6.09,  the  panel  load  at  Lr 
The  maximum  positive  shears  are : 

Vl  =    ^^(1  +2  +  3  +  4  +  5)=   +15.22 


111 


102 


BRIDGE  ENGINEERING 


.09 


.09 


34-4)=   +10.15 


(1  +  2  +  3)  =   +6.09 


=      i(i  +  2)  =   +3.05 

D 

and  the  maximum  web  stresses  are  found  to  be: 

L0Ut  =  -15.22  X  1.28  =  -19.50 

U,L2  =  +10.15  X  1.28  =  +13.00 

U2L3  =  +   6.09  X  1.28  =  +    7.80 

U3Lt  =  +    3.05  X  1.28  =  +    3.91 

U2L2  =   -  6.09 
U3L3  =   -  3.05 

It  is  unnecessary  to  compute  the  shears  further  than  one  panel  past 
the  middle  of  the  span,  as  only  the  maximum  stresses  are  usually 
required. 

The  wind  stresses  from  various  causes  are  grouped  together  and 
given  in  Table  X. 

From  Table  X  it  is  seen  that  large  wind  stresses  occur  in  some 
of  the  members.  Most  specifications  require  that  the  stresses  due  to 
wind  shall  be  neglected  in  the  design  unless  they  exceed  25  per  cent 
of  the  sum  of  the  dead-load  and  live-load  stresses. 

The  subject  of  wind  stresses  does  not  ordinarily  receive  the  con- 
sideration it  should  have;  in  fact,  it  appears  to  be  common  practice, 
in  the  case  of  spans  up  to  200  feet,  to  neglect  the  action  of  the  wind  in 
all  members  of  the  bridge  except  the  top  and  bottom  lateral  diagonals, 
the  top  struts,  the  portal,  and  the  bending 
effect  in  the  end-post.      For  the  last  two 
effects  mentioned,  see  the  next  succeeding 
article. 

54.  Portals  and  Sway  Bracing.  One- 
half  of  the  wind  on  the  top  chord  is  trans- 
ferred to  the  hips  UlfUl  and  Ue'U6.  From 
there  it  is  carried  to  the  abutments  by 
means  of  the  portal  bracing  and  the  end- 
posts.  Various  styles  of  portal  bracing  are 
in  use,  but  few  are  so  easily  analyzed  and 
constructed  as  that  of  Fig.  101.  This  form 


Fig.  101.  Style  of  Portal 
Bracing  in  Common  Use  on 
Spans  up  to  250  Feet. 


112 


BRIDGE  ENGINEERING 


103 


TABLE  X 
Wind  Stresses  in  Pratt  Truss 

WEB  MEMBERS 


OVERTURNING 

LaU, 

C/.L,          [7,1,3 

U,L, 

[/,£, 

r/,L, 

U3L, 

Wind  Right 

! 

on  Truss 

-14.08 

0               0 

o 

0 

0 

0 

on  Train 

-19.50 

-13.00 

+  7.80 

+  3.91 

+  6.09 

-6.09 

-3.05 

Wind  Left 

on  Truss 

+  14.08 

0               0 

0 

0 

0 

0 

on  Train 

+  19.50 

-13.00  :  -7.80    -3.91 

-6.09 

+  6.09 

+  3.05 

Maximum 

+  Stress 

+  33  .  58 

+  13.00  ;  +7.80 

+  3.91 

+  6.09 

+  6.09 

+  3.05 

Maximum 

-  Stress 

-33.58 

-13.00  :  -7.80 

-3.91 

-6.09 

-6.09 

-3.05 

CHORDS 


MEMBER 

L0Lt             L,L,            L,L3 

U,U2 

U,U3 

Direct 

Wind  Right 

0     +8.82 

+  14.12 

0 

+    5.29 

0  ,  +26.46 

+  42.36 

Wind  Left 

-   8.82 

-14.12 

-15.88 

-    5.29 

-    7.06 

-26.46 

-42.36     -47.64 

Overturning  Truss 
Wind  Right 

+    8.80 

+    8.80 

+    8.80 

-    8.80 

-    8.80 

Wind  Left 

-    8.80 

-    8.80 

-   8.80 

+    8.80 

+    8.80 

Overturning  Train 
Wind  Right 

+  12.12 

+  12.12 

+  19.39 

-19.39 

-21.82 

Wind  Left 

-12.12 

-12.12 

-19.39 

+  19.39 

+  21.82 

Maximum 

+  Stress 

+  20.92 

+  56  .  20 

+  84.67 

+  28.19 

+  35.91 

Maximum 

-  Stress 

-56.20 

-77.40 

-91.71 

-33.48 

-37.68 

LATERAL  SYSTEMS 


MEMBER 

Ui'U, 

U,'U, 

UjU, 

U3'U3 

L0'Ll 

Lt'L. 

L,'L3 

Wind  Right 
on  Truss 

+  6.95 

+  2.32 

-3.0 

-1.5 

+  11.60 

+    6.95 

+    2.32 

on  Train 

+  34.75 

+  23.15 

+  13.91 

Wind  Left 

on  Truss 

0 

0 

-3.0 

-1.5 

0 

0 

0 

on  Train 

0 

0 

0 

Maximum 

+  6.95 

+  2.32 

-3.0 

-1.5 

+  46.35 

+  30  ..10 

+  16.23 

The  stresses  -in  L,'L,,  L,'L,,  and  L3' L3  are  not  given  in  the  above  table.  These 
members  are  the  floor-beams,  and  the  small  stress  due  to  wind  is  neglected  in  their 
design. 


113 


104  BRIDGE  ENGINEERING 

of  portal  is  at  present  being  used  almost  universally  on  all  spans  up 
to  250  feet. 

Let  it  be  required  to  analyze  a  portal  of  this  form,  all  the  dis- 
tances being  as  indicated  in  Fig.  101  ;  and  let  : 

w  =  Wind  panel  load  of  upper  chord; 
m'  =  Number  of  panels  in  upper  chord; 
Then, 

P  =  (mr  -  l)w; 
and, 


V  =   ±       (P  +  w)  +  w  ; 

also, 

Hl  =  H2  =   {  (P  +  w)  +  w  J-  -=-  2. 

The  stress  in  BC,  the  center  of  moments  being  at  D,  is: 


Q  \  2    a   \ 

The  stress  in  AB,  the  center  of  moments  being  at  E,  is: 

,     wa  +  HJ  .      I 

SAB  =    +  -  —  =   +w  +  H, • 

a  a 

For  the  stress  in  BD,  the  center  of  moments  is  taken  at  C,  and 
the  perpendicular  distance  c  to  BD  is  determined.  The  stress  in 
BD,  then,  is: 

2  c 
The  stress  in  BE  is: 

SBE  =  -  //,  A- 

It  must  be  remembered  that  A,  is  not  the  height  of  the  truss, 
but  is  the  length  of  the  end-post  from  L0  to  Uv 

For  the  truss  of  Article  47,  w  =  1.5;  m'  =  4;  and  P  =  4.5. 
The  value  h,  =  (202  +  252)*  -  32.0  feet.  The  distance  a  must  be 
so  chosen  that  BD  will  not  interfere  with  engines  or  other  traffic 
which  passes  through  the  bridge.  It  will  be  assumed  as  5  feet  in 

this  case.    Then  V  =  (4.5  +  1.5  +  1.5)  ^  =  14.08;  and  Hl  -  H2 

7'5  0-7* 

=  —   =  3.75;  whence, 

SBC  =  -  ( 6.0  +  3.75  X  ^-\  =   -  26.25 


114 


BRIDGE  ENGINEERING 


105 


SAB  =  1.5  +  3.75  X  ~ 
o 


+  21.75 


2  +   5.02  =    9.85. 


The  distance  BD  =  ^BC~  +   CD    = 
Then,    from    similar    triangles    DCB  and  DFC,  is   obtained    the 
proportion : 

CF  _  BC . 

CD~BD' 

C= —  =  4. 3  feet;  and 

32  0 

SBD  =   +3.75  X  -.     •   =   +27.90 
4  .6 


SBB=   -3.75  X 


=    -27.90 


When  the  wind  blows  from  the  other  side,  the  stresses  in  the 
diagonals  are  reversed,  and  those  in  the  top  are  transposed.  The 
members  shown  by  broken  lines  take  no  stress.  When  the  wind 
blows,  the  end-posts  tend  to  bend  as  shown  in  Fig.  102.  This  is  with- 


\ 


Fig.  102.    Illustrating  Tendency 
of  End-Posts  to  Bend  under 
Wind  Load. 


Fig.  103.    Bending  Tendency 

when  End-Posts  are  Fixed 

at  Lower  End. 


stood  by  the  cross-section  of  the  post  at  the  points  E  and  D.  The 
bending  moment  caused  at  these  points  by  the  wind  is  Hi  X  I  and 
H2  X  /.  For  the  truss  under  consideration, 

MD  =  ME  =  3.75  X  27  X  12  =  1  215  000  Ib.-ins. 
If  the  posts  are  fixed  at  the  lower  end,  then  they  will  tend  to 
bend  as  shown  in  Fig.  103,  the  post  resisting  the  bending  at  two 
points  D  and  d.  The  section  at  each  point  withstands  in  this  case 
only  half  of  the  moment  just  computed,  or  1  215  000  +  2  =  607  500 
Ib.-ins.  A  further  discussion  of  this  will  be  given  in  Part  II,  on 
"Bridge  Design." 


115 


106 


BRIDGE  ENGINEERING 


Various  forms  of  sway  bracing  are  used  to  connect  the  inter- 
mediate posts  and  thus  stiffen  the  cross-section  of  the  bridge  at  those 
points.  The  form  of  portal  just  given  is  often  used,  as  is  also  the 
form  shown  in  Fig.  104.  Here  h  is  the  height  of  the  truss.  The 
braces  BD  are  called  knee-braces.  Here  w  is  the  wind  panel  load  of 

the  top  chord,  and 


2wh 


2w 


,  =  _  (wa  +  H2l)  -=-  a 


,c,  =  +  (W  +  Hi  — ) 
a 


The  stress  in  B'B  is  the  direct 
compression  due  to  wind  right  or 
Fig.  104.   A  Type  of  Portal  and  Sway      left,    and    differs    in     accordance 

Bracing  in  Frequent  Use.  .  ,       ,  ...  c     , 

with  the  position  of  the  top  strut. 
There  is  also  a  bending  moment  at  Br  and  B,  which  is: 

Ms,  =  MK  =  -V'g  +  HJi. 

The  bending  moment  at  D  and  D'  is  equal  to  H2l  or  Hj,  -r-  2, 
according  to  whether  or  not  the  lower  ends  of  the  posts  are  fixed. 

The  determination  of  the  stresses  for  the  truss  of  Article  47  is 
left  to  the  student. 

When  the  wind  is  from  the  other  side  of  the  truss,  the  signs  of 
the  stresses  in  the  knee-braces  and  the  members  C'B'  and  CB  are 
reversed. 

55.  Final  Stresses.  The  class  of  stresses  which  go  to  make 
up  the  maximum  or  minimum  for  which  the  member  is  designed r  is 
.determined  by  the  specifications  used.  The  dead-load  and  live-load 
stresses  are  always  included,  and  then  those  due  to  impact  and  wind 
should  be  added  if  required.  In  computing  the  maximum  stresses, 
the  algebraic  sum  should  always  be  used.  In  a  large  majority  of 
cases,  all  stresses  which  go  to  make  up  the  maximum  have  the 


116 


BRIDGE  ENGINEERING  107 

same  sign,  but  some  exceptions  have  been  noted,  as  in  the  middle 
vertical  of  a  Pratt  or  Howe  truss.  The  minimum  stresses  ure,  with 
rare  exceptions,  obtained  by  combining  stresses  with  signs  of  opposite 
character. 

GIRDER  SPANS 

56.  Moments  and  Shears  in  Floor=Beams.  In  any  bridge  the 
floor-beam  acts  as  a  support  for  either  the  joists  or  stringers,  and  the 
moments  and  shears  occurring  in  it  are  due  to  the  loads  which  come 
on  the  joists  or  stringers.  In  a  highway  bridge  the  joists  are  spaced 
so  closely  that  the  load  which  they  transmit  to  the  floor-beams  may 
be  considered  as  uniformly  distributed,  providing  the  live  load  is  a 
uniform  load,  in  which  case, 

_    (2PL  +  Pn)  X  panel  length  in  inches 

8 

V  =  (2PL  +  PD)  +•  2, 

where    M  =  Maximum  moment  in  pound-inches; 
V  =  Maximum  shear; 
PL  =  Live  panel  load; 
PD  =  Weight  of  stringers  and  floor  material  in  one  panel. 

It  will  be  seen  that  these  formulae  are  those  for  the  maximum 
moment  and  shear  in  a  uniformly  loaded  beam,  the  total  load  being 
2PL+PD. 

As  an  example,  let  it  be  required  to  determine  the  maximum 
moment  and  shear  in  the  floor-beam  of  a  highway  bridge  whose  panels 
are  20  feet  long,  and  trusses  16  feet  center  to  center,  the  live  load 
being  100  pounds  per  square  foot  of  floor  surface,  the  flooring  weighing 
10  pounds  per  square  foot,  and  there  being  5  lines  of  joists  weighing 
15  pounds  per  linear  foot,  and  2  lines  of  joists  weighing  8  pounds  per 
linear  foot. 

PL  =  1JL  x  20  X  100  =  16  000  pounds. 

PD  =  5  X  20  X  15  +  2  X  20  X  8  +  16  X  20  X  10  =  5  020  pounds. 
Therefore, 

(2  X  16000  +  5  020  }  20  X  12 

~T~~ 

=  1  110  600  pound-inches  at  center  of  floor-beam. 
V  =  (2  X  16  000  +  5  020)  -H  2 

=  18  510  pounds  at  ends  of  floor-beam. 


117 


108 


BRIDGE  ENGINEERING 


In  the  case  of  a  single-track  railroad  bridge,  there  are  only  two 
stringers  upon  which  the  weight  of  the  track,  the  engine,  and  the 
train  is  supported.  These  join  the  floor-beam  at  points  equally 
distant  from  the  center  of  same.  The  weight  of  the  ties,  rails,  and 
fastenings  is  usually  taken  at  400  pounds  per  linear  foot  of  one 
track.  As  regards  the  live  load,  the  proposition  reduces  itself  to 
placing  the  wheel  loads  so  that  the  sum  of  the  reactions  of 
stringers  in  the  adjacent  panels  will  be  a  maximum  on  the  floor- 
beam  under  consideration.  This  is  discussed  in  Article  47,  page  87 
(see  Fig.  94). 

In  determining  the  values  of  the  maximum  moment  and  shear  in 
the  floor-beam,  the  case  is  that  of  a  beam  symmetrically  loaded  with 
two  equal  concentrated  loads.  Each  load  is  equal  to  the  dead  weight 
of  one  stringer,  one-half  the  track  weight  in  one  panel,  and  the  maxi- 
mum sum  total  of  the  reactions  due  to  the  wheel  loads  on  the  stringers 

in  adjacent  panels  which  meet  at 
that  point.  This  latter  quantity  is 
called  the  floor-beam  reaction.  For 
a  general  arrangement  of  the  loads, 
see  Fig.  105.  The  distance  a  has 
become  standard  for  single-track 
spans,  and  is  6  feet  6  inches. 

Let  it  be  required  to  determine 
the  maximum  shears  and  moments 
in  the  floor-beam  of  the  truss  of 
Article  47. 

The  weight  of  the  stringer  may  be  obtained  by  the  formula  of 
Table  II,  and  is: 

Stringer  =  20  (123.5  +  10  X  20)  -f-  2  =  3  200  pounds. 
The  weight  of  one-half  of  the  ties,  rails,  etc.,  in  one  panel  is: 
i  Track  =  (400  X  20)  +  2  =  4  000  pounds. 

The  weight  that  comes  from  the  engine  wheels  is  given  in  Article 
47,  page  87  (see  Fig.  94),  and  is  65.55.  Each  load  is  therefore  the 
sum  of  all  the  above  weights,  as  follows: 

3  200  +  4  000  +  65  550  =  73  750. 

The  maximum  shear  (see  Fig.  105)  is  seen  to  be  73  750  pounds; 
and  the  maximum  moment  occurs  at  C  and  D,  and  is: 


° 

0 

p 

1 

Kl 

r- 

C/ 

/-51m 
1 

qers' 

iD 

Floor 

3eam 

C. 

a-<b'.5 

5I7R 

toC.  of 

Trussc 

Fig.  105.    Arrangement  of  Loads  for  Cal 

culating  Moments  and  Shears 

in  Floor-Beams. 


118 


BRIDGE  ENGINEERING 


109 


M  =  73  750   X 


X  12  =  4  646  250  pound-inches. 


For  any  particular  engine  the  floor-beam  reactions  for  different 
length  panels  are  easily  tabulated  for  future  reference.  Table  XI 
gives  the  floor-beam  reactions  for  panel  lengths  from  10  to  24  feet 
inclusive. 

TABLE  XI 

Floor-  Beam  Reactions 
E  40  Loading 


PANEL 
LENOTH 

MAXIMUM 

FLOOR-BM. 
REACTION 

PANEL 
LE  NOTH 

MAXIMUM 
FLOOR-BM. 
REACTION 

PANEL 
LENGTH 

MAXIMUM 
FLOOR-BM. 
REACTION 

10 

41000 

15 

55000 

20 

65.55 

11 

43800 

16 

57000 

21 

67.10 

12 

46600 

17 

59000 

22 

69.20 

13 

44400 

18 

61000 

23 

71.30 

14 

52200 

19 

63000 

24 

73  40 

In  many  cases  it  is  desirable  to  keep  the  dead-load  shears  and 
moments  separate  from  those  of  the  live  load ;  and  this  can  easily  be 
done. 

In  neither  of  the  above  cases  has  the  weight  of  the  beam  itself 
been  taken  into  account.  This 
should  be  done  in  the  final  design. 
The  method  of  procedure  is  to 
compute  the  moment  and  shears 
as  above;  then  make  a  provisional 
design  of  the  beam.  Next,  com- 
pute the  weight  of  the  beam  thus 
designed,  and  add  the  moments 
and  shears  caused  by  this  weight 
to  the  other  dead-load  moments 
and  shears;  then  re-design  the  beam 
and  compute  its  weight.  If  this 

last  weight  varies  10  per  cent  from  the  previous  weight,  another  re- 
design should  be  made.  The  above  proceeding  belongs  to  Bridge 
Design,  Part  II,  and  will  there  be  treated. 

57.  Moments  in  Plate=Girders.  Plate  girders  are  of  two  classes 
— namely  (1)  those  which  have  the  ties  or  floor  laid  directly  upon  the 
upper  flanges  of  the  girders;  these  are  called  deck  plate-girder  bridges; 


Fig.  106.    Cross-Section  of  Deck  Plate- 
Girder  Railway  Bridge. 


119 


110 


BRIDGE  ENGINEERING 


and  (2)  those  in  which  the  webs  of  the  girders  are  connected  with 
each  other  at  intervals  by  floor-beams  which  in  turn  cany  stringers 
or  joists  in  exactly  the  same  manner  as  in  the  floor  system  of  a 
railroad  or  highway  truss-bridge;  this  latter  type  is  called  a  through 
plate-girder  bridge.  Figs.  106  and  107  show  cross-sections  of  deck 

and  through  plate- 
girder  bridges  re- 
spectively, for  rail- 
way service.  Fig. 

108  is  a  side  view 
of    a    deck   plate- 
girder  bridge.    Fig. 

109  is  a  longitudinal 
section  of  a  through 
plate-girder  rail- 
road bridge.     The 

section  is  taken  down  the  middle  of  the  track.  The  bridge  shown  has 
5  panels.  An  odd  number  of  panels  should  be  chosen,  as  this  does 
not  bring  a  floor-beam  at  the  center  of  the  span,  and  hence  the  great 
moment  which  would  then  be  caused  is  avoided. 

The  analysis  of  the  shears  and  moments  of  a  through  plate- 
girder  is  precisely   the  same  as  that  for  a  truss  bridge.     The  shear  is 


Fig.  107.    Cross-Section  of  Through  Plate-Girder  Railway 
Bridge. 


=£ 

vt  htf   bj* 

to  M  M  \; 

m  M  wi 

*A  id  m  m 

*l  $ 

Fig.  108.    Side  View  of  Deck  Plate-Girder  Railway  Bridge. 

constant  between  any  two  panel  points  as  0-1  or  1-2,  etc.,  and  the 
moments  are  computed  for  the  points  1,  2,  3,  and  4. 

If  wheel  loads  are  used  for  moments,  the  relation  that  K  =  — 

Wn  m 

-Lmustbe+,   and    that   k  = (L  +  P)  must   be-,   holds 

m 

true  when  the  loads  are  in  correct  position  for  maximum  moments. 
Here  m  =  the  number  of  panels,  and  n  =  the  panel  under  considera- 


120 


BRIDGE  ENGINEERING 


111 


tion  and  is  to  be  reckoned  from 
the  left  end;  in  fact,  all  terms 
have  the  same  value  as  men- 
tioned in  Article  46.  A  careful 
review  of  Articles  44  and  46 
should  enable  the  student  to 
follow  the  example  which  will 
now  be  given. 

EXAMPLE.  It  is  required 
to  determine  the  moments  at 
the  points  of  floor-beam  support 
for  a  5-panel  through  plate- 
girder  of  75-foot  span.  The 
live  loading  is  Cooper's  E  40. 

Dead-Load  Moments. 
Through  plate-girders,  on  ac- 
count of  the  heavy  floor  system 
and  the  fact  that  the  floor  sys- 
tem transfers  its  own  weight 
and  that  of  the  live  load  to  the 
girders  as  concentrated  loads, 
are  about  40  per  cent  heavier 
than  deck  plate-girder  bridges 
of  the  same  span.  The  weight 
of  the  entire  span,  therefore,  is; 

1.4  X  75  (123 . 5  +  10  X  75)  = 
91  700  pounds. 

Part  of  this  91  700  pounds  (the 
weight  of  the  girders  themselves) 
acts  as  a  uniform  load ;  the  re- 
mainder (the  weight  of  the 
floor-beams  and  stringers)  acts 
as  concentrated  loads  at  the 
points  where  the  floor-beams 
join  the  web.  Experience  has 
shown  that  the  weight  of  the 
floor  for  a  single-track  railroad 
system  is  about  400  pounds 


121 


112 


BRIDGE  ENGINEERING 


TABLE  XII 
Wheel  Position,  Moments  in  a  Through  Plate-Gird* 


PANEL  11 
POINT  | 

WHEEL 

AT 

POINT 

L 

Wn 

' 

£  +  p 

K 

k 

REMARKS 

1 
1 
1 
1 
1 

2 

3 
4 
5 
6 

10 
30 
40 
40 
40 

f-3,', 

1|?  -  38.4 
o 

2f=- 

TT  -  40  4 

f  =  39.0 
o 

20 
20 
20 
20 
13 

30 
50 
60 
60 
53 

+ 

+ 
+ 

+ 

Maximum 
Maximum 
Maximum 

152  X  2        60  S 

20 

70 

_|_ 

179  y  9 

i/w    A    ^           AQ      Q 

90 

90 

O 

152  X  3 

103 

172  X  3 

116 

192  X  3 

129 

O 

129  X  4 

7 

ino 

142  X4 

1  1  (\ 

152  X  4 

1  ^ 

1  49 

129 

152  X  4 

1  "3 

1  49 

5 

per  linear  foot.  The  weight  of  the  stringers  and  floor-beams  for 
this  bridge  is  therefore  75  X  400  =  30  000  pounds,  and  91  700  - 
30  000  =  61  700  pounds  acts  as  a  uniform  load.  This  61  700  pounds 
is  distributed  over  two  girders,  and  so  gives  61  700  -r-  (2x75)  =  say, 
412  pounds  per  linear  foot  of  one  girder. 

The  dead  load  which  is  concentrated  at  each  panel  point  is  that 
due  to  the  weight  of  the  steel  floor  and  the  weight  of  ties,  rails,  and 
fastenings.  It  is,  for  one  girder, 

15  X  (400  +  400)  H-  2  =  6  000  pounds. 


122 


Jan 

fm 

till 

is'I 

I  si 

Isst 

si!! 


—  — 

W  Ofi 

P  ill* 


BRIDGE  ENGINEERING 


113 


The  dead-load  moments  are  now  computed  by  the  methods  of 
Strength  of  Materials,  and  are  found  to  be : 

M0  =  Ms  =  0; 

Ml  =  M4  =  +4  390  000  pound-inches; 

M 2  =  M 3  =  +6  580  000  pound-inches. 

Live-Load  Moments.  The  positions  of  the  wheels  for  maximum 
moments  are  now  determined  (see  Table  XII). 

The  computations  for  the  reactions  are  best  arranged  in  tabular 
form.  Table  XIII  gives  the  values. 

TABLE  XIII 
Reactions  for  a  Through  Plate-Girder 


H 

O 

1 
1 

2 

3 
3 

5 

1 

Oi*.W  AT  I 
|  POINT  | 

EQU/ 

TION* 

FOR  REACTION 

REAC- 
TION 

8 
fi 
R 

=  (6  708 
=  (7668 
=  (8  728 

+  192 
+  212 

+  232 

X 
X 
X 

4)  + 
4  - 

75 
10  X  78)  *  75 
10  X  83  -  20  X  75)  +  75 

99.7 
103.2 
97.8 

4 

7 

R 

=  (4632 

+  152 

X 

7)  •*• 

75 

76.0 

R 
R 

=  (4  632 
=  (5848 

+  152 
+  172 

X 
X 

6)  -5- 
3)  + 

75 
75 

73.9 
84.9 

4 

4 
4 

6 

7 
8 

R 

li 
1! 

=  (2  851 
=  (3  496 
=  (4  632 

+  129 
+  142 
+  152 

X 

•' 

X 

4)  -!- 

4)  ^ 

2)  * 

75 
75 

75 

44.9 
54.2 
65.4 

. 
' 


The  live-load  moments  are  computed  as  follows: 

"Wheel  3,  M  =  99  .7  X  15  -  230  =  1  265  BOO  pound-feet. 
Wheel  4,  M  =103.2  X  15  -     20'  X  5    -   20    X    10    =     1247000 
Point  !•(      pound-feet. 

Wheel  5,  M  =  97.8  X  15  -     20  X  5    -    20    X    10    =     1  167  000 

pound-feet. 

Point  2    Wheel  4,  M  =  76  .0  X  30  -     480  =  1  800  000  pound-feet. 

f  Wheel  6,  M  =  73.9  X  45  -  1  640  =  1  785000  pound-feet. 

[Wheel  7,  M  =  84.9  X  45  -  2  155  =  1  665000  pound-feet. 

(Wheel  6,  M  =  44.9  X  60  -  1  640  =  1  054  000  pound-feet. 

Point  4^  Wheel  7,  M  =  54.2  X  60  -  2  155  =  1  097  000  pound-feet. 

I  Wheel  8,  M  =  65.4  X  60  -  2  851  =  1  073  000  pound-feet. 

•  The  above  values  show  that  the  greatest  live-load  moments  ares 

M  at  Point  1,  by  wheel  3  =  1  265  000  pound-feet 
Mat      "     2,"       "     4  =  1800000      "      " 
Mat      "     3,  "       "     4  =  1800000      "      " 
Mat      "     4,  "       "     3  =  1265000      "      " 


114  BRIDGE  ENGINEERING 

The  last  two  values  are  obtained  when  the  load  comes  on  the  bridge 
from  the  left.  Inspection  of  the  results  obtained  at  points  3  ami  4 
when  the  load  comes  on  from  the  right,  shows  that  they  are  con- 
siderably smaller  than  the  results  obtained  at  their  symmetrical 
points  1  and  2,  and  therefore  it  was  not  necessary  to  determine  the 
moments  for  any  points  to  the  right  of  the  center.  This  is  true  of  all 
girder  spans,  deck  or  through. 

The  method  of  procedure  when  the  girder  is  a  deck  plate-girder 
is  the  same  as  that  just  illustrated,  except  that  in  the  computation 
of  the  dead-load  moments  there  is  no  concentration  of  certain  por- 
tions of  the  dead  load,  the  weight  of  the  girders  themselves  being  a 
uniform  load,  as  is  also  the  weight  of  the  ties  and  rails  or,  if  it  be  a 
highway  bridge,  the  floor-joists  which  run  transversely.  Highway 
spans  are  seldom  built  of  deck  plate-girders,  it  being  preferable  to 
use  the  through  girders,  as  then  the  girders  themselves  serve  as  a  rail- 
ing and  keep  the  traffic  confined  to  the  roadway.  The  girder  span  is 
usually  divided  into  ten  equal  divisions,  the  points  of  division  being 
called  the  tenth-points.  The  shears  and  moments  are  computed  for 
the  center  point  and  those  points  which  lie  to  the  left  of  the  center. 
After  the  values  are  computed,  they  are  laid  off  as  ordinates,  with  the 
corresponding  tenth-points  as  abscissae.  A  curve  is  then  drawn 
through  their  upper  ends,  and  the  curve  of  maximum  shears  or 
moments  is  the  result.  To  get  the  maximum  shear  or  moment  at 
any  point  other  than  a  tenth-point,  the  ordinate  is  scaled  at  the 
desired  point. 

EXAMPLE.  Let  it  be  required  to  determine  the  maximum 
moments  at  the  tenth-points  of  a  100-foot-span  deck  plate-girder. 

Dead-Load  Moments.  The  weight  of  steel  in  the  span  is  100 
(123.5  +  10  X  100)  =  112  350  pounds,  and  the  weight  of  the  track 
is  400  X  100  =  40  000  pounds,  making  a  total  of  152  350  pounds, 
or  152  350  ^  (2  X  100)  -  say,  762  pounds  per  linear  foot  per  girder. 
The  dead-load  moments  are  now  determined  according  to  the  methods 
of  Strength  of  Materials,  and  are  : 

M,  =  342  800  pound-feet 


A/3  =  799  840      "      " 
M4  =  914  100      "      " 
Ms  =  952200       "       " 
Live-Load   Moments.     The   determination   of  the    wheel   load 


124 


BRIDGE  ENGINEERING 


115 


Wn 
positions  is  made  by  the  use  of  the  formulae  K  =  ( L)  and 

k  = (L  +  P) ;  only,  in  this  case,  n  is  the  number  of  divisions 

ra 

from  the  left  support  to  the  section,  and  ra  is  the  number  of  divisions 
into  which  the  girder  is  divided. 

The  determination  of  the  wheel  positions  is  given  in   Table  XIV. 

TABLE  XIV 
Wheel  Positions,  Moments  in  Deck  Plate-Girder 


1 
1 

WHEEL 

AT 

POINT 

L 

Wn 

P 

L  +  P 

K 

k 

REMARKS 

1 
1 
1 

1 
1 
1 

2 
3 
4 
5 
6 

7 

10 
20 
20 
20 
20 
13 

258  X  0.1  =  25.8 
261  X  0.1  =  26.1 
254  X  0.1  =  25.4 
242  X  0.1  =  24.2 
240  X  0.1  =  24.0 
230  X  0.1  =  23.0 

20 
20 
20 
20 
13 
13 

30 
40 
40 
40 
33 
26 

+ 
+ 
+ 
+ 
+ 
+ 

- 

Maximum 

2 
2 
2 
2 

o 
3 
4 
5 

10 

30 
50 
60 

232  X  0.2  =  46.4 
245  X  0.2  =  49.0 
258  X  0.2  =  51.6 
261  X  0.2  =  52.2 

30 
20 
20 
20 

30 
50 

70 
80 

+ 
+ 
+ 

+ 

Maximum 

3 
3 
3 
3 

3 

4 
5 
6 

30 
50 
70 
80 

232  X  0.3  =  69.6 
232  X  0.3  =  69.6 
245  X  0.3  =  73.5 
261  X  0.3  -  78.3 

20 
20 
20 
13 

50 
70 
90 
93 

+ 
+ 
+ 

+ 

Maximum 

4 

4 

4 
4 
4 

4 
5 
6 

7 
8 

50 
70 
90 
103 
106 

212  X  0.4  =  84.8 
232  X  0.4  =  92.8 
245  X  0.4  =  98.0 
258  X  0.4  =  103.2 
261  X  0.4  =  104.4 

20 
20 
13 
13 
13 

70 
90 
103 
116 

119 

+ 
+ 
+ 

+ 

+ 

Maximum 

6 
5 
5 
6 
5 
5 
5 
5 
5 

6 

7 
8 
9 
10 
11 
12 
13 
14 

90 
103 
116 
129 
132 
102 
102 
102 
122 

232  X  0.5  =  116.0 
232  X  0.5  =  116.0 
245  X  0.5  =  127.5 
258  X  0.5  =  129.0 
274  X  0.5  =  137.0 
244  X  0.5  =  122.0 
234  X  0.5  =  117.0 
224  X  0.5  =  112.0 
234  X  0.5  =  117.0 

13 
13 
13 
13 
10 
20 
20 
20 
20 

103 
116 
129 
142 
142 
122 
122 
122 
132 

+ 
+ 
+ 
0 

+ 
+ 
+ 

+ 

+ 

0 
0 

Maximum 

While  many  wheels  on  point  1  satisfy  the  condition,  the  greatest 
moment  will  occur  when  one  of  the  large  drivers  is  at  the  point,  and 
it  is  therefore  unnecessary  to  examine  the  point  for  other  wheels. 
The  same  is  true  at  the  center  point,  5,  the  maximum  occurring  under 
one  of  the  heavy  driver  wheels.  The  reactions  and  the  computations 
for  the  same  are  given  in  Table  XV. 


125 


116 


BRIDGE  ENGINEERING 


TABLE  XV 
Reactions  for  a  Deck  Plate-Girder 


POINT 

WHEEL  AT 
POINT 

EQUATION  FOR  REACTION 

REACTION 

1 

1 
1 
1 

2 
3 
4 
5 

R  =  (12041  +  5  X  258)  H-  .100 
R  =  (12  599  +  4  X  261)  -^  100 
R  =  (11  984  +  4  X  254)  -;-  100 
R  =  (11  334  +  4  X  234  -=-  2  X  4"  -  2)  -  100 

133.31 
136.43 
130.00 
122  .  86 

2 
2 

3 
4 

#  =    12041  H-100 
#  =  (12  041  +  5  X  258)  +  100 

120.41 
133.31 

3 
3 

4 
5 

R  =  10816  -H  100 
R  =  12  041  -i-  100 

108.16 
120.41 

4 
4 
4 

5 
6 

7 

R  =     (8  728  +  4  X  232)  +  100 
fl  =  (10  816  +  4  X  245)  -r-  100 
fl  =  (12  041  +  4  X  258)  H-  100 

96.56 
117.96 
130.73 

5 
5 
5 
5 
5 
5 
5 

7 
8 
9 
10 
11 
12 
13 

R  =   (8  728   +      8  X  232)  -5-  100 
fl  =  12041    -100 
72  =(12041  +      5X  258)  -  100 
R  =(13904  +      2X  274)  +  100 
fl=(11334+     5X234  +  2X     52  H-  2)  -f-  100 
fl  =    (9  514  4-   10  X  214  +  2  X  102  -s-  2)  H-  100 
R  =    (7794  +    15  X  194  +  2  X  152  -5-  2)  -t-  100 

105.84 
120.41 
133.31 
144.52 
125.29 
117.54 
109.29 

TABLE  XVI 
Maximum  Moments  in  a  Deck  Plate-Girder 


POINT 

WHEEL 
POINT 

EQUATION  FOR  MOMENT 

MOMENT  IN 
POUND-FEET 

1 
1 

1 
1 

2 
3 
4 
5 

M  = 

M  = 
M  = 
M  = 

133.31  X  10 
136.43  X  10 
130.00  X  10 
122.86  X  10 

-  80 
-  5  X  20 
-  5  X  20 
-  5  X  20 

1  253  100 
1  264  000 
1  200  000 
1  128  000 

2 
2 

3 

4 

M  = 
M  = 

120.41  X  20 
133.31  X  20 

-  230 

-  480 

2  178  200 
2186200- 

3 
3 

4 
5 

M  = 

M  = 

108.16  X  30 
120.41  X  30 

-  480 
-  830 

2  764  800 

2  782  300 

4 
4 
4 

5 
6 
7 

M  = 
M  = 

M  = 

96  .  56  X  40 
117.96  X  40 
130.73  X40 

-  830 
-  11  640 
-  2  155 

3  032  400 
3  078  400 
3  074  200 

5 
5 
5 
5 
5 
5 
5 

7 
8 
9 
10 
11 
12 
13 

M  = 
M  = 
M  = 
M  = 

M  = 
M  = 
M  = 

105.84  X  50 
120.41  X  50 
133.31  X  50 
144  .52  X  50 
125.29  X  50 
117.54  X  50 
109.29  X  50 

-  2  155 
-  2851 
-  3496 
-  4072 
-  3068 
-  2658 
-  2248 

3  137  000 
3  169  500 
3  169  500 
3  154  000 
3  196  500 
3219000 
3  216  500 

126 


BRIDGE  ENGINEERING  117 

Table  XVI  gives  the  computations  of  the  live-load  moments  at 
the  tenth-points,  the  final  results  being  in  pound-feet. 

Whenever  any  loads  were  off  the  left  end  of  the  bridge,  the  lines 
7  to  16  of  the  engine  diagram  were  used  (Fig.  85).  For  example,  with 
wheel  10  at  5,  wheel  1  would  be  off  the  left  end.  By  looking  in  the 
second  space  of  line  8,  there  is  found  the  quantity  13  904,  which  is 
the  moment  of  wheels  2  to  18  inclusive  about  a  point  directly 
under  wheel  18.  Just  to  the  right  of  the  vertical  line  through 
wheel  18,  is  the  value  284,  which  is  the  weight  of  wheels  1  to  18  in- 
clusive; but  this  must  be  decreased  by  10,  the  weight  of  wheel  1,  as 
that  wheel  is  off  the  span.  As  wheel  18  is  2  feet  from  the  right  end 
of  the  girder,  the  moment  about  the  point  is  13  904  +  274  X  2.  By 
looking  in  the  second  space  of  line  16,  the  value  4  072  is  found.  This 
is  the  value  of  the  moment  of  loads  2  to  9  inclusive  about  a  point 
directly  under  wheel  10,  and  must  be  subtracted  from  the  moment 
of  the  reaction  in  order  to  get  the  moment  at  5  for  this  loading. 
See  Articles  21  and  47  for  further  information  regarding  the  use  of 
the  values  in  lines  7  to  16  of  the  engine  diagram. 

By  the  help  of  differential  calculus  it  can  be  proved  that  the 
greatest  possible  moment  does  not  occur  at  the  middle  of  a  beam  loaded 
either  with  concentrated  loads  or  with  concentrated  loads  followed  by 
a  uniform  load,  but  it  occurs  under  the  load  nearest  the  middle  of  the 
beam  when  the  loads  are  so  placed  that  the  middle  of  the  beam  is  half 
way  between  the  center  of  gravity  of  all  the  loads  and  the  nearest  load. 

The  wheel  which  produces  this  greatest  moment  is  the  same  one 
which  produces  the  maximum  moment  at  the  middle  of  the  beam. 
The  exact  solution  of  this  problem  involves  the  use  of  quadratic 
equations,  but  for  all  practical  purposes  the  following  rule  will 
suffice : 

Place  the  loading  so  that  the  wheel  which  produces  the  maximum 
moment  at  the  middle  of  the  beam  is  .at  that  point.  Find  the  distance  of  the 
center  of  gravity  of  all  the  loads  from  the  right  end.  Move  the  loads  so  that 
the  middle  of  the  beam  is  half  way  between  the  center  of  gravity  as  found 
above  and  the  load  which  produced  the  maximum  moment  at  the  middle 
of  the  beam.  Find  the  moment  under  that  load,  with  the  loads  in  the  position 
just  mentioned. 

For  the  case  in  hand,  wheel  12  at  5  gives  the  maximum  moment. 
The  moment  at  the  right  end  of  the  span,  wheel  12  being  at  5,  is: 
9  514  +  10  X  214  +  2  xT(J2  -s-  2  =  11  754  000  pound-feet. 


187 


118  .       BRIDGE  ENGINEERING 

The  center  o/  gravity  is  —  -  =  50.2  feet  from  the  right  sup- 

/o4 

port,  or  0.2  foot  to  the  left  of  the  center  of  the  girder.  Now  place 
whee'  12  one-tenth  of  a  foot  to  the  right  of  the  center,  and  deter- 
mine the  moment  under  it.  The  reaction  will  be : 

R  =  (9  514  +  9.9  X  214  +  2  X  97I)2  -f-  2)  -*-  100  =  117.306; 
and, 

M  =  117.306  X  50. 1  -  2  658  =  3  219  306  pound-feet. 

In  this  particular  case  the  difference  between  the  greatest 
moment  possible  and  the  greatest  moment  af  the  middle  is  not 
sufficient  to  warrant  the  extra  labor  involved  in  computing  it.  In 
general  it  may  be  said  that  if  the  greatest  moment  possible  occurs  within 
six  inches  of  the  middle  of  the  beam,  it  is  not  necessary  to  compute  it, 
the  moment  at  point  5  being  taken. 

58.  Shears  in  Plate=0iirders.  In  the  case  of  through  plate- 
girders,  the  maximum  live-load  shears  are  determined  by  placing  the 

wheels  in  such  a  position  that  Q  =  -  G  is  -f,  and  q  —  — 

(G  +  P)is-. 

In  these  equations,  m  is  the  number  of  panels  into  which  the 
span  is  divided;  and  the  other  quantities  are  the  same  as  given  in 
Article  45,  which  should  now  be  reviewed. 

For  example,  let  it  be  required  to  determine  the  dead  and  live 
load  shears  in  the  through  plate-girder  of  Article  57,  p.  111. 

The  weight  of  one  girder  =  61  700  -f-  2  =  30  850  Ibs. 
"        "        "    *  the  floor  =  5  X  6  000  =  30  000  Ibs. 


Total  weight  on  one  girder  =  00  850  Ibs. 

The  dead-load  shears  are  then  computed  by  the  methods  given  in 
Strength  of  Materials,  and  are  given  as  follows,  it  being  remembered 
that  the  concentrated  load  which  comes  at  the  end  is  one-half  a  panel 
load,  or  3000  pounds:  ' 

Vu  =  60  850  ~  2  =  30  475  Ibs.  =  end  shear; 

on  Q  CQ 

V\  =  30  475  -  3  000  -     -  =21  305  Ibs.; 

O 

V,  =  30  475  -  3  000  -  6  000  -  2  X  —  f—  =  9  135  Ibs. 

o 


V3  =  30  475  -  3  000  -  2  X  6  000  -  2  X  =  3  135  Ibs. 

T'c  =  0, 


128 


BRIDGE  ENGINEERING 


119 


where  F0  =  the  shear  at  the  end ;  Vl  =  the  shear  just  to  the  left  of 
point  1;  V.,  =  the  shear  just  to  the  left  of  point  2;  F3  =  the  shear 
just  to  the  right  of  point  2 ;  and  Vc  =  the  shear  at  the  middle  of  the 
girder. 

The  determination  of  the  wheel  load  position  for  maximum 
live-load  shears  is  given  in  Table  XVII.  By  comparing  the  formulae 
Q  and  K,  it  will  be  seen  that  for  the  first  panel  Q  =  K,  and  q  =  k, 
as  n  =  1.  The  position  of  wheel  loads  for  maximum  moments  at 
point  1  is  the  same  as  for  maximum  shear  in  the  first  panel.  Accord- 
ing to  Table  XII,  wheels  3;  4,  and  5  at  point  1  all  give  maximum 
shears  in  the  first  panel.  In  this  case,  as  in  previous  ones,  only  the 
shear  for  the  first  position  of  the  loading  found-  for  any  particular 
point  will  be  determined,  as  the  difference  between  this  and  the  other 
cases  is  too  small  to  warrant  the  additional  labor  necessary  in  com- 
puting them.  It  is  evidently  unnecessary  to  go  past  panel  3,  as  only 
the  maximum  shears  are  required. 

TABLE  XVII 

Wheel  Positions,  Shears  in  a  Through  Plate-Girder 

.    (m  =  5) 


WHEEL 

w 

POINT 

AT 

G 

P 

P+G 

<f 

q 

REMARKS 

POINT 

1 

\ 

See  Table  XII,  and 

text  above  this  table 

2             2 

10 

142  -r-  5  =  28.4      20 

30 

+ 

Maximum 

2         ;           3 

30 

152  H-  5  =  30.4 

20 

50 

+ 

— 

Maximum 

2             4 

40 

152  -  5  =  30.4 

20 

60 

— 

— 

3 

2 

10 

116  H-  5  =  23.2 

20 

30 

+ 

_ 

Maximum 

3             3 

30 

116  -r-  5  =  23.2      20 

50 

— 

~~ 

For  wheel  3  at  point  1,  the  left  reaction  (see  Table  XIII)  is  99.7. 
That  portion  of  wheels  1  and  2  which  is  transferred  to  point  0  is 
230  -T-  15  =  15.33;  and  the  shear  in  the  first  panel,  therefore,  is: 

y,  =  99.70  -  15.33  =   +84.37. 
For  wheel  2  at  point  2,  the  left  reaction  is: 

R  =  (3  496  +  142  X  5)  -  75  =  56. 10; 
therefore, 

F,-  56.10  -|^  =  +  50.67. 


129 


120 


BRIDGE  ENGINEERING 


A  computation  with  wheel  3  at  point  2  will  give  a  shear  only  560 
pounds  greater,  which  difference  \vould  not  influence  the  design  to 
any  appreciable  extent. 

For  wheel  2  at  point  3,  the  left  reaction  is: 

R  =  (2  155  +  116  X  1)  -  75  =  30.30; 
therefore, 


30.3  _«. 


+  24.97. 


When  the  girder  is  a  deck  one,  the  computation  of  the  dead 
shears  is  very  much  simplified,  as'  all  of-  the  load  is  uniform. 


Fig.  110.    Beam  under  Wheel  Loads  Followed  by  Uniform  Load. 

Let  it  be  required  to  determine  the  dead  and  live  load  shears 
at  the  tenth-points  of  the  deck  plate-girder  of  Article  57. 
The  total  weight  of  one  girder  and  track  is  76  175  Ibs. 

F0  =  76  175  -5-  2  =   +38  088  pounds. 

+  30  470  pounds. 


=  38088-^ 


10 


V2  =  38  088  -  —  X  76  175  =  +22  450  pounds. 
V3  =  38  088  -  ~  X  76  175  =  +  15  230  pounds. 
Y4  =  38  088  -  ~  X  76  175  =+  7  618  pounds. 


The  position  of  the  wheel  loads  to  produce  the  maximum  shear 
cannot  be  determined  by  the  same  relation  as  that  used  in  structures 
which  have  a  system  of  floor-beams  and  stringers,  for  here  not  a 
portion,  but  all  of  'the  load  to  the  left  of  the  section,  must  be  sub- 
tracted from  the  left  reaction  in  order  to  give  the  shear. 


180 


BRIDGE  ENGINEERING  121 

The  correct  relation  for  the  wheel  load  position  will  now  be 
deduced. 

Let  Fig.  1  10  represent  a  beam  of  span  I  loaded  with  a  series  of 
wheel  loads  followed  by  a  uniform  load.  Let  P  equal  the  weight  of 
the  first  wheel,  W  equal  the  weight  of  all  the  loads,  and  g  the  distance 
from  the  center  of  gravity  of  all  of  the  loads  to  the  right  abutment. 
The  distance  between  the  first  and  second  wheel  centers  is  a,  and  the 
first  wheel  is  at  the  section  b  -  b  at  a  distance  xl  from  the  left  support. 
Then, 

7?  '       W9-- 

R,  --J-; 

and 

F'b_h  =  /?/  -  (loads  to  left  of  section)  =  5^. 

Now,  assume  that  the  loads  move  forward  the  distance  a.  The 
wheel  2  will  be  at  section  b-b,  and  Fig.  Ill  will  represent  the 
position  of  the  loads.  Then, 

W(g+  a}. 
it,     -  l 

and 

y"b_b  -  R"  -  P 

W  (g  +  a)  . 

I 

_  Wg       Wa 
~     I       h    /     ' 

It  is  now  evident  that  in  order  to  get  the  greatest  shear  at  section 
b-b,  wheel  2  must  be  placed  at  the  section  whenever  F"b_b.is 
greater  than  F'b  _  b.  Then, 


Now,  canceling  out  the  term  —'  ~  ,which  appears  on  both  sides  of  the 
equation,  there  results: 

£>>. 

For  the  engine  under  consideration,   a  =  8  feet,  and  P  =  10  000 
pounds,  and  the  equation  reduces  to  : 


131 


122  BRIDGE  ENGINEERING 


which  is  to  say  that  when  the  load  on  the  girder  is  greater  than  1£ 
times  the  span,  then  wheel  2  should  be  placed  at  the  section  in  order 
to  give  the  maximum  shear. 

For  loading  E  40,  the  following  is  true: 

For  all'  sections  up  to  and  including  the  center  of  all  spans,  place 
wheel  2  at  the  section  to  give  the  maximum  shear. 

In  Fig.  Ill  it  is  immaterial  whether  or  not  any  additional  loads 
come  on  the  span  at  the  right  end  when  the  loads  move  forward  the 


Fig.  111.    Beam  of  Fig.  110  with  Loads  Moved  Forward. 

distance  a,  as  they  would  only  tend  to  increase  the  left  reaction  and 
therefore  the  shear  P7/'b_b.  If  the  relation  deduced  is  true  for  the 
case  when  no  extra  loads  come  on  at  the  right  end,  it  will  be  true 
when  they  do. 

The  live-load  shears  at  the  left  end  and  at  the  tenth-points, 
wheel  2  being  at  the  section  in  all  cases,  are  computed  from  the  gen- 
eral formula,  which  is: 

V  =  R  -  2  P, 
in  which, 

R  =  Left  reaction; 

~  P  =  All  loads  to  left  of  section,  and  is  equal  to  10  000  pounds  for 
all  sections  except  the  end  of  the  girder. 

The  computations  and  results  can  be  conveniently  placed  in 
tabular  form,  and  are  given  in  Table  XVIII. 

In  order  to  illustrate  the  use  of  the  relation  W>  1— ^  I,  let  point 

3  in  the  above  span  be  taken.  Place  wheel  2  at  point  3;  then,  as 
wheels  1  to  13  are  on  the  girder,  the  total  weight  W  is  212.  As  I  = 
100,  \\l  =  125.  Therefore,  as  212  is  greater  than  125,  wheel  2  is 
the  correct  wheel. 


132 


BRIDGE  ENGINEERING 


123 


TABLE  XVIII 
Maximum  Shears  in  a  Deck  Plate-Oirder 


g         REACTION  EQUATION 

R 

!,- 

V 

REMARKS 

^  1 

0 

(13  904  +  4X274)  -100 

150.00 

0 

150.00 

Wheel 

18,  4  ft.  from  rt.  end 

1 

2 

(12041+5X258)  +  100 
10816  +  100 

133.31    10 
108.16!  10 

123.  31  1   Wheel 
98.16    Wheel 

16,  5  ft.  from  rt.  end 
15  at  right  end 

3 

(  7  668  +  4X212)  -100 

85.16;  10 

75.16    Wheel 

13,  4  ft.  from  rt.  end 

4 

(  5  848  +  4X172)  -100 

65.36    10 

55.36    Wheel 

1  1,  4  ft.  from  rt.  end 

5 

(  4  632  +  2X152)  -100 

49.36   10 

39.36!  Wheel 

10,  2  ft.  from  rt.  end 

The  curyes  of  maximum  live-load  moments  and  shears  are  shown 
in  Fig.  112.  They  should  always  be  drawn.  From  them  the  shear 
or  moment  at  any  desired  section 
can  be  determined.  For  exam- 
ple, let  it  be  desired  to  determine 
the  maximum  live-load  shear  and 
moment  at  a  point  24  feet  from 
the  left  end  of  the  girder.  By 
drawing  the  ordinate,  shown  by 
a  broken  line  in  Fig.  112,  and 
scaling,  the  following  values  are 
found : 

F24    =  88  000  pounds; 

A/24  =  2  440  000  pound-feet. 

A  similar  set  of  curves  for 
the  dead-load  shears  and  moments 
should  be  made.  The  set  for  the 
deck  plate-girder  in  hand  is  shown 
in  Fig.  113.  These  are  easily 
constructed  by  laying  off  the  max- 
imum values  of  the  shear  at  the 


Fig.  112.     Curves  of  Maximum  Live-Load 
Moments  and  Shears. 


end,  and  the  maximum  value  of 

the  moment  at  the  center.     The 

shear  curve  is  a  straight  line  from  the  end  to  the  center,  while  the 

moment  curve  is  a  parabola  from  the  center  to  the  end. 

The  stresses  in  the  lateral  systems  of  plate-girders  are  computed 
in  a  manner  the  same  as  that  employed  for  the  lateral  systems  of 
trusses,  the  unit-load  being  taken  according  to  the  specifications  used. 


133 


124 


BRIDGE  ENGINEERING 


59.  Stresses  in  Plate=Qirders.  The  stresses  in  plate-girders 
are  treated  in  the  Instruction  Paper  on  Steel  Construction,  Part  IV, 
pages  251  to  263,  and  the  student  is  referred  to  this  treatise  for  infor- 
mation regarding  this  subject. 

The  stress  in  the  flange  is  seen  to  depend  upon  the  distance  from 
center  of  gravity  to  center  of  gravity.  This  distance,  in  turn,  depends 


Pounds 
Fig.  113.   Curves  of  Dead-Load  Shears  and  Moments  in  a  100-Foot  Span  Deck  Plate-Girder. 

upon  the  depth  of  the  girder.  Certain  approximate  rules  have  been 
proposed  in  order  to  determine  this,  but  the  following  formula  will 
give  the  width  of  the  web  plate  in  accordance  with  best  modern 
practice : 

7 


in  which 


0 . 005  I  +  0 . 543  ' 


d  =  Width  of  the  web  plate,  in  the  even  inch; 
I  =  Span,  in  feet. 


For  example,  let  it  be  required  to  determine  the  width  of  the 
web  plate  of  a  plate-girder  of  80-foot  span  center  to  center  of  end 
bearings. 

d  =  0.005X80  +  0.543  =  0^4  =  85'2  (say  86)  inches' 
If  the  resultant  value  had  been  85  inches,  the  width  would  have  been 
taken  as  either  84  or  86.  The  reason  for  this  is  that  the  wide  plates 
kept  in  stock  at  the  mills  are  usually  the  even  inch  in  width  and  can 
therefore -be  procured  more  quickly  than  if  odd -inch  widths  were 
ordered,  in  which  case  the  purchaser  would  be  forced  to  wait  until 


134 


BRIDGE  ENGINEERING 


125 


they  were  rolled — often  a  period  of  several  months.  The  distance 
back  to  back  of  flange  angles,  the  so-called  depth  of  girder,  is  one-half 
inch  more  than  the  width  of  the  web.  This  is  due  to  the  fact  that 
each  pair  of  flange  angles  extend  one-fourth  inch  beyond  the  edge  of 
the  web  plate,  so  as  to  keep  any  small  irregularities  caused  on  the 
edge  of  the  web  plate  by  the  rolling,  from  extending  beyond  the  backs 
of  the  angles. 

EXERCISES  AND  PROBLEMS 

1.  Determine  the  maximum  positive  shears  in  the  first  six  panels  of 
a  9-panel  114-foot  Pratt  truss,  the  live  panel  load  being  8.0.  Use  the  exact 
and  also  the  conventional  method. 

ANSWER: 


x 

XACT       HEARS 

N              I                              RS 

F, 

16 

+  32.00 

+  32.00 

V2 

14 

+  24.54 

+  24.90 

V3 

12 

+  18.05 

+  18.70 

V4 

10 

+  12.48 

+  13.35 

V, 

8 

+    7.85 

+    8.90 

vl 

6 

+    4.50    ' 

+    5.34 

2.  Find  the  maximum  and  minimum  stresses  in  L,C/2  and   U3L3  of  an 
8-panel  160-foot  through  Warren  truss.     Height  20  ft.;  dead  panel  load  10.00, 
all  on  lower  chord;  live  panel  load  12.00. 

ANSWER:  In  LJJ2:  d.  1.,  -28.00;  1.1.,  -  35. 30 and  +1.68; 
max.,  -63. 30;  min.,  -26.32.  In  t/3L3:  d.  1.,  +16.80;  l.l.,  +  25. 20 
and  -5. 04; max.,  +42. 00; min.,  +  11.76. 

3.  In  the  truss  of   Problem  2,  determine  the  maximum  stress  in  L2L3 
by  the  method  of  moments,  and  also  by  the  tangent  method. 

ANSWER:  d.  1.  =  +67.50;    1.1.  =  +81.00;    max.  -  +148.50. 

4.  Determine  the  dead-load  stresses  in  the  members  U2L2  and    L4U6 
of  a  9-panel  180-foot  through  Warren  truss.       Height  is  24  feet;  dead  panel 
load  is  10.0,  one-third  being  at  each  panel  point  of  the  upper  chord,  and  two- 
thirds  being  at  each  panel  point  of  the  lower  chord. 

ANSWER:    U^L,  =  +30.60;   LfJ.  =  -1 .80. 

5.  Determine  the  stress  in  the  counter  of  a  through   Howe  truss  of  8 
panels  and  160-foot  span.       Height  is  30  ft.;  dead  panel  load,  9.6;  live  panel 
load;  11.5. 

ANSWER:     —4.59. 


135 


126 


BRIDGE  ENGINEERING 


6.     In  the  truss  of  Problem  5,  determine  the  maximum  and  minimum 
stress  in  U2L2,  L2U3,  and  L3U4. 

ANSWER: 


V,L, 

w. 

wr. 

d.  1. 

+  20  .  80 

-17.30 

-    5.76 

1.1. 

+  30.30                     -25.90 

-17.30 

1.1. 

-14.40                      +5.18 

0.00 

Max. 

+  15.10 

-43.20 

-23.06 

Min. 

+  19.36 

-21.20 

±0.00 

6  at  IO'=  60' 


Fig.  114.    Deck  Parabolic  Bowstring  Truss. 

7.  In  the  deck  parabolic  bowstring  truss  of  Fig.  114,  determine  the 
maximum  stress  in  L,L2,  L,E/2,  and  U3L3.  The  dead  panel  load  is  4.0,  all 
on  upper  chord;  and  the  live  panel  load,  20.0. 

ANSWER:    L^  =  +201 .9;  LJj\  =  +21 .8;    U3L3  =  —  33.6. 


L, 


6  at  1 5= 90' 


Fig.  115.    Through  Bowstring  Truss. 

8.  In  the  through  bowstring  truss  of  Fig.  115,  determine  the  maximum 
stress  in  U^  and  LjC72,  the  dead  panel  load  being  5.0,  and  the  live  panel 
load  15.0. 


ANSWER:     U^  =  +33.50;    LJJ2  =  +38.0. 


136 


BRIDGE  ENGINEERING 


127 


9.  Determine  the  maximum  and  minimum  stresses  in  the  members 
_Z7,L,,  t/,L2,  t/,L2,  and  U3L3  of  a  7-panel  175-foot  through  Pratt  truss  30  feet 
high.  Dead  panel  load  is  10.0,  all  on  lower  chord;  live  panel  load  is  15.0. 

ANSWER  : 


•V, 

** 

W! 

U,L. 

d.  1.                  +10.0 

+  26  .  00 

-10.00 

0.00 

1.  1. 

+  15.0 

+  41.70 

-21.40 

-12.85 

1.1. 

0.0 

-   2.78 

+    6.42 

0.00 

Max. 

+  25.0 

+  67.70 

-31.40 

-12.85 

Min. 

+  10.0 

+  23.22 

-    3.58 

0.00 

10.  Determine  the  maximum  and  minimum  stresses  in  the  members 
Ujnv  m3L3,  U2L2,  and  m2U2  of  the  deck  Baltimore  truss  shown  in  Fig.  116. 
Dead  panel  load,  30  000  Ibs.;  live  panel  load,  50  000  Ibs.  One-third  of  dead 
panel  load  is  applied  at  the  lower  ends  of  all  the  verticals. 

ANSWER  : 


CT.m, 

m3L3 

L\L3 

m,U, 

d.  1. 
1.  1. 
1.1. 

+  19058 
+  333  .  5 
-    15.1 

+    84.8 
+  191.5 
-    50.5 

-110.0 
-211.0 
+    10.7 

+  21.2 
+  56.6 
0.0 

Max. 
Min. 

+  524  .  3 

+  175.7 

+  276.3 
+    34.3 

-321.0 
-    99.3 

+  56  .  6 
+  21.2 

11.  In  the  truss  of  Problem  10,  determine  the  maximum  stress  in 
M2U2  and  L3L4.  , 

ANSWER:    M2£72  =  -840.0;    L3L4  =  +960.0. 

12.  Determine  the  position  of  the  wheel  loads  of  Cooper's  E  40  loading 
to  produce  the  maximum  positive  live-load  shears  in  the  panels  of  a  7-panel 
175-foot  Pratt  truss. 

ANSWER  :   Lv  wheel  4 ;  L2,  wheels  3  and  4 ;  L3,  wheel  3 ;  L4,  wheel 
3;   L5,  wheel  2;    Lv  wheel  2. 

13.  Determine  the  maximum    positive  live-load  shears  for  the  truss 
of  Problem  12. 

ANSWER:     Vl  =  192.8;    F2  =  137.8;    F3  =  90.8;   F4  -  52.6; 
F6=25.0;    F.=  6.8. 


137 


128 


BRIDGE  ENGINEERING 


14.  Determine  the  position  of  the  wheel 
loads  of  Cooper's  E  40  loading  to  produce  max- 
imum moments  at  the  panel  points  of  the  truss 
of  Problem  12. 

ANSWER;  Lv  wheel  4;  Lv  wheel  7; 
L3,  wheels  11  and  12;  L4,  wheels  13  and 
14. 

15.  Determine  the  maximum  moments  at 
the  panel  points  of  the  truss  of  Problem  12. 
Loading,  Cooper's  E  40. 


ANSWER:     Mt 


4820000;     M2  = 


7745000;      M3   =   9192000;      M4  =  • 
9  082  000,  all  in  pound-feet. 

1G.  Compute  the  maximum  live-load  web 
stresses  in  the  truss  of  Problem  12,  the  height 
being  32  feet.  Loading,  E.  40. 

17.  Compute  the  maximum  live-load  chord 
stresses  in  the  truss  of  Problem  12,  the  height 
being  32  feet.     Loading,  E  40. 

18.  Compute  the  impact  stresses   for  all 
members  of  the  truss  of  Problem  12. 

19.  Determine    the    maximum     live-load 
shears  at  the  tenth-points  of  a  65-foot   span 
deck  plate-girder.     Loading,  E  40. 

ANSWER:  F0  -  103.0;  Vl  =  86;  F2 
=  69.7;  F3  =  54.5;  F4  -  40.8;  F5  = 

28.4. 

20.  Compute  the  shear  due  to  impact  in 
the  girder  of  Problem  19. 

ANSWER:  F0  =  84.7;  V\  =  71.5;  F2 
-58.8;  F3  =  47.0;  F4=  35.6;  F5  = 
25.4. 

21.  Compute     the     maximum     live-load 
moments  at  the  tenth-points  of  the  girder  of 
Problem  19.     Loading,  Cooper's  E  40. 


138 


BRIDGE  ENGINEERING 


129 


ANSWER: 


POINT 

WHEEL 

MOMENT 

IMPACT  MOMENT 

1 

2 

6540 

5520 

2 

2 

11  320 

9520 

3 

3 

14860 

12500 

4 

4 

16850 

14050 

5 

4 

16860 

14530 

1  .  45'  from  center 

4 

16920 

14650 

All  moments  are  in  thousands  of  pound-inches. 


139 


BRIDGE  ENGINEERING 

PART  II 


BRIDGE    DESIGN 

60.  General  Economic  Considerations.  The  prime  considera- 
tion which  influences  the  decision  to  build  is  cost.  After  the  decision 
to  build  has  been  made,  the  problem  is  one  of  a  purely  engineering 
character,  whereas  in  the  first  case  it  was  one  of  either  a  political  or 
an  engineering  character,  or  both.  The  engineering  problem  is  an 
economic  one,  in  which  maximum  benefits  must  be  obtained  at  a 
minimum  cost. 

A  map  of  the  proposed  bridge  site  and  the  approaches,  as  well 
as  of  the  country  for  a  considerable  distance  up  and  down  stream, 
should  be  made.  This  map  should  show  the  contours,  the  soundings, 
the  borings,  the  high  and  low  water-mark  elevations,  and  the  excep- 
tional flood  line.  On  this  map  the  bridge  should  be  plotted  in  its 
proposed  location  and  also  in  various  others.  In  the  case  of  each  of 
these  locations,  various  schemes  taking  into  account  different  numbers 
of  piers  and  spans  should  be  considered. 

Several  authors  have  attempted  to  present  formulse  having  a 
more  or  less  theoretical  derivation  and  purporting  to  indicate  the 
correct  number  of  piers  and  spans  for  a  minimum  cost.  The  use  of 
these  formulse  should  not  be  encouraged,  since  they  do  not  in  any  case 
give  results  close  enough  to  serve  for  anything  but  a  rough  guide. 

The  cost  of  abutments  will  vary  somewhat  with  the  location  and 
the  character  of  the  approach.  This  variation  is  usually  small,  and 
ordinarily  an  approximate  location  of  the  abutments  can  be  quickly 
made.  As  the  number  of  abutments  is  in  all  cases  constant,  their 
effect  upon  the  problem  of  the  location  of  the  bridge  is  small,  the  main 
proposition  being  that  of  the  cost  and  the  number  of  piers  and  spans. 

The  cost  of  the  piers  will  usually  not  be  constant,  those  closer  to 
the  middle  of  the  stream  costing  more  on  account  of  the  depth  of  the 
water  and  the  more  difficult  character  of  the  foundation.  Piers 

Copyright,  1908,  by  American  School  of  Correspondence. 


141 


BRIDGE  ENGINEERING 


should  not  be  placed  on  a  skew;  neither  should  they  be  placed  directly 
in  the  maximum  line  of  action  of  the  current.  If  a  skew  is  unavoid- 
able, it  should  be  as  small  as  possible.  The  cost  of  piers  should  be 
ascertained  by  the  most  careful  estimates.  In  the  case  of  small 
bridges  where  there  are  only  one  or  two  piers,  the  matter  is  very  simple, 
but  with  a  considerable  number  of  piers  the  problem  becomes  very 
complicated  and  requires  weeks  and  sometimes  months  or  years  for 
its  solution. 

The  determination  of  the  cost  of  the  superstructure  is  a  com- 
paratively simple  matter.  In  certain  instances  the  class  of  bridge  is 
limited  to  some  extent  by  the  specifications.  Cooper,  in  Article  2  of 
his  "Specifications  for  Steel  Railroad  Bridges  and  Viaducts"  (edition 
of  1906),  gives  the  following: 

Types   of   Bridges    for  Various   Spans 


SPANS 

KIND  op  BRIDGE 

Up  to     20  feet 
20  to     75      " 
75  to  120     " 
120  to   150     " 
Over      150     " 

Rolled  beams 
Riveted  plate-girders 
Riveted  plate-  or  lattice-girders 
Lattice  or  pin-connected  trusses 
Pin-connected  trusses 

One  railroad  expresses  a  preference  for  plate-girders  for  all  spans 
from  20  to  115  feet;  and  for  spans  from  there  to  150  feet,  riveted 
trusses. 

The  question  as  to  whether  the  bridge  will  be  deck  or  through 
is  one  which  is  decided  by  the  controlling  influences  of  water-way, 
false  work,  time  of  erection,  and  extra  cost  of  masonry.  If  the  clear 
height  required  for  the  water-way  is  sufficiently  small,  the  deck 
bridge  should  be  chosen,  as  in  this  class  the  cost  of  false  work  is  less, 
the  time  of  erection  is  less,  and  the  cost  of  masonry  is  less  by  an  amount 
equal  to  the  cross-section  of  the  piers  times  the  depth  of  the  truss. 
Deck  bridges  also  cost  less  than  through  bridges  of  equal  span. 

The  conditions  permitting,  girders  should  be  used  in  preference 
to  trusses.  While  for  equal  spans  girders  are  heavier  and  therefore 
cost  more,  the  steel  work  alone  being  considered,  little  or  no  false 
work  is  required,  and  the  time  of  erection  is  much  less  than  in  the 


142 


BRIDGE  ENGINEERING  133 

case  of  trusses.  This  makes  the  total  cost  of  girder  bridges  less  than 
those  in  which  trusses  are  used.  Another  item  in  favor  of  girders  is 
their  great  stiffness. 

While  pin-connected  bridges  cost  less  and  are  easier  to  erect, 
their  stiffness  is  not  so  great  as  that  of  riveted  bridges,  which  cost 
more.  The  time  required  for  the  erection  of  riveted  bridges  is  also 
greater  than  that  for  pin-connected  bridges.  This  is  on  account  of 
the  great  amount  of  time  required  to  make  the  riveted  connections. 
For  long  spans,  say  over  200  feet,  it  is  necessary  to  use  pin-connected 
bridges,  as  the  extreme  size  of  the  connection  plates  prohibits  the  use 
of  the  riveted  type.  Also,  it  is  unnecessary  to  use  riveted  long-span 
trusses  to  obtain  stiffness,  as  the  weight  of  the  pin-connected  bridges 
is  so  great  when  compared  with  the  live  load  that  sufficient  stiffness 
is  obtained. 

The  cost  of  spans  of  different  lengths  and  character  may  be 
obtained  directly  from  the  bridge  companies;  or  their  weights  may 
be  computed  from  the  formulae  given  in  Article  20,  p.  9  (Part  I, 
"Bridge  Analysis"),  and  multiplied  by  the  unit  price  which  your 
experience  indicates  is  correct,  thus  giving  the  total  cost. 

Evidently  the  solution  of  problems  of  this  nature  cannot  be 
made  within  the  limits  of  this  text,  but  the  following  example  will 
tend  to  indicate  somewhat  the  manner  of  procedure  in  a  problem  of 
this  kind.  For  example,  if  the  length  between  abutments  is  1  400  ft., 
the  cost  of  each  abutment  is  $12  000,  and  the  cost  of  each  pier  is 
$15  000,  then,  if  we  have  fourteen  100-foot  plate-girder  spans,  each 
costing  $4  300,  and  thirteen  piers,  the  total  cost  will  be  $279  200.  On 
the  other  hand,  if  nine  piers  and  ten  140-foot  truss  spans,  each  cost- 
ing $9  200,  are  used,  the  cost  will  be  $251  000,  showing  a  balance  of 
$28  200  in  favor  of  the  truss  scheme.  The  live  loading  is  E  50. 

61.  Economic  Proportions.  The  depth  of  girders  is  given  in 
Article  59,  Part  I. 

In  the  case  of  trusses,  the  effect  of  an  increase  in  the  height 
is  to  increase  the  stresses  in  the  web  members  and  to  decrease  the 
stresses  in  the  chord  members.  This  variation  does  not  affect  the 
weights  to  any  considerable  extent;  in  fact,  a  variation  of  20  per  cent 
in  the  height  will  not  affect  the  weight  more  than  2  or  3  per  cent. 

The  height  of  the  bridge  is  usually  fixed  by  some  considerations 
which  are  in  turn  determined  by  the  specifications.  The  height  must 


143 


134 


BRIDGE  ENGINEERING 


be  sufficient  to  clear  whatever  traffic  will  pass  through.  It  should 
also  be  sufficient  to  prevent  overturning  on  account  of  the  wind 
pressure  on  the  truss  or  on  the  traffic.  In  addition,  the  height  of  the 
bridge  is  influenced  by  the  depth  of  the  portal  bracing.  A  deep 
portal  bracing  is  desirable,  in  that  it  stiffens  the  trusses  under  the 
action  of  the  wind  and  the  vibration  due  to  the  passing  traffic;  but 
a  deep  portal  bracing  increases  the  height  of  the  truss  and  therefore 

the  bending  in  the 


Panel  Length 
18  toes  feet. 

/ 

end-posts  due   to 
the  wind.     Judg- 
ment on  the  part 
of    the    engineer 
should  be  used  in 
order  to  determine 
the  limiting  height 
for  securingamax- 
imum  amount  of 
benefit  as  regards 
stiffness      and     a 
minimum  amount 
of  bad  effect  due 
to  the  bending  in 
the  end-posts.  Fig. 
117,  which    gives 
the  height  for  any 
given    length     of 
span,  may  be  said 
Variations  of  a  foot 

c 

Double  Track 

y 

y 

_£ 

I 

-Stnqle  Track 

^ 

Sf 

an  in  f«et. 

3               50                               .100                                ISO                             £0 

117.    Curves  Showing  Relation  between  Height  of  Truss 
and  Length  of  Span  in  Double-  and  Single-Track 
Railway  Bridges. 

represent  the  best  modern  practice  (1908). 

Pig 


or  more  from  those  given  do  not  affect  the  weight  to  any  appreciable 
extent. 

The  distance  from  center  to  center  of  trusses  for  highway 
bridges  depends  upon  the  width  of  the  street  or,  if  in  the  country, 
the  width  of  the  roadway.  Streets,  of  course,  vary  in  width  in  differ- 
ent localities,  but  country  highway  bridges  usually  have  a  roadway  of 
from  14  to  16  feet  in  the  clear. 

In  the  case  of  railroad  bridges,  the  distance  from  center  to  center 
of  trusses  depends  upon  whether  the  track  is  straight  or  on  a 
curve,  and  also  upon  whether  the  bridge  is  a  deck  or  a  through  bridge. 


144 


BRIDGE  ENGINEERING  135 

The  actual  amount  varies  in  most  cases,  and  is  fixed  by  specification. 
Some  specifications  require  that  when  the  track  is  straight,  the  dis- 
tance from  center  to  center  of  trusses  shall  be  17  feet;  or  that,  in  case 
one-twentieth  of  the  span  exceeds  the  17  feet,  then  one-twentieth  of 
the  span  shall  be  used. 

For  deck  plate-girders  the  common  practice  appears  to  be  to 
space  them  as  given  below : 

Width  of  Plate-Ciirder   Bridges  for  Various  Spans 


SPANS 

DISTANCE  CENTER  TO  CENTER  OF 
PLATE-GIRDERS 

Up  to    65  feet 
65    to    80     " 
80   to  115     " 

6  feet  6  inches 
7  feet  0  inches 
7  feet  6  inches 

For  through  plate-girders  the  spacing  should  be  such  that  no 
part  of  the  clearance  diagram  will  touch  any  part  of  the  girder.  In 
case  of  double-track  plate-girders  with  one  center  girder,  great  care 
should  be  exercised  in  order  that  the  center  girder  shall  not  be  so  deep 
nor  have  so  wide  a  flange  as  to  interfere  with  the  clearance  diagram 
(see  Fig.  126). 

On  account  of  the  wind  on  a  train  which  runs  on  track  placed 
at  the  elevation  of  the  top  chord  of  deck  bridges,  the  overturning 
effect  is  exceedingly  great,  and  special  care  should  be  taken  that  the 
height  and  width  are  such  as  to  prevent  overturning. 

In  through  bridges  the  clearance  must  be  such  as  to  allow  the 
clearance  diagram  to  pass.  Special  attention  should  be  paid  to  the 
knee-braces  and  also  to  the  portal  braces.  When  the  bridge  is  on  a 
tangent,  the  spacing  of  the  trusses  is  a  comparatively  simple  matter, 
being  just  sufficient  for  the  clearance  diagram;  but  on  curves,  allow- 
ance must  be  made  for  the  tilt  of  the  diagram  due  to  the  super- 
elevation of  the  outer  rail,  and  also  allowance  must  be  made  for  the 
fact  that  the  length  of  the  cars  between  trucks  forms  a  chord  to  the 
curve,  and  as  such  the  middle  ordinance  must  be  taken  into  account. 
It  is  also  necessary  to  allow  for  that  part  of  the  car  which  projects 
over  the  trucks,  as  this  will  extend  beyond  the  outer  rail  by  an  amount 
greater  than  one-half  the  width  of  the  clearance  diagram.  (See 
Figs.  119  and  120.) 


145 


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137 


62.  The  Clearance  Diagram. 
The  clearance  diagram  is  not 
supposed  to  represent  the  outline 
of  the  largest  engine  or  car  which 
may  run  over  the  line,  but  repre- 
sents the  maximum  amount  of 
space  which  may  be  taken  up  by 
objects  which  are  to  be  shipped 
over  the  line.  For  instance,  the 
lower  part  of  the  clearance  dia- 
gram may  allow  for  snow-plow 
or  ballast  distributors,  and  the 
upper  part  may  take  into  account 
the  passage  of  such  material  as 
carloads  of  lumber,  piles,  or  tele- 
graph poles.  The  standard  clear- 
ance diagram  of  the  Lehigh 
Valley  Railroad  is  given  in  Fig. 
118.  This  diagram  is  for  the 
clearance  on  straight  track  only. 
On  curves,  the  diagram  tilts  as 
shown  in  Fig.  119,  and  to  allow  for  this  tilting  the  Lehigh  Valley 
Railroad  requires  2j  inches  additional  clearance  on  the  inside  of 
curves  for  each  inch  of  elevation  of  the  outer  rail.  In  addition  to  this 
tilting  effect,  the  clearance  should  also  be  increased  on  account  of  the 


Fig.  119.    Clearance  Diagram  on  Curves, 
Showing  Tilting. 


Fig.  120.    Standard  Car  on  Curve,  Showing  Necessity  for  Wider  Spacing  of  Trusses. 

length  of  the  cars  and  their  projection  over  the  outer  and  inner  rails. 
Fig.  120  shows  a  standard  car  according  to  the  specifications  of  the 
American  Railway  Engineering  &  Maintenance  of  Way  Association, 
in  such  a  position  on  a  single-track  span  as  to  show  the  effect  of  the 
curve  upon  the  widening  of  the  spacing,  center  to  center  of  trusses. 


147 


138  BRIDGE  ENGINEERING 

This  car  is  80  feet  long,  60  feet  between  centers  of  trucks,  and  is  as 
wide  as  the  clearance  diagram,  14  feet  for  single  track.  It  is  evident 
that  the  trusses  cannot  be  spaced  so  as  to  interfere  with  the  clear- 
ance line  of  the  body  of  the  car  and  its  projecting  ends.  These 
clearance  lines  are  represented  as  broken  lines  in  Fig.  120,  and  are 
marked  c-c.  Note  that  the  center  of  the  track  is  seldom  in  the  center 
of  the  floor-beam.  Also,  it  is  evident  that  the  sharper  the  curve, 
the  greater  the  required  distance  between  trusses,  and  accordingly 
the  greater  the  floor-beams  in  length.  This  varies  the  moment  in  the 
different  floor-beams  and  therefore  makes  them  more  costly.  The 
stringers,  also,  are  more  costly,  on  account  of  the  fact  that  their  ends 
are  skewed.  On  account  of  the  eccentricity  of  the  track,  one  truss 
takes  more  of  the  load  than  the  other,  and  therefore  the  trusses  are 
not  the  same — a  fact  which  further  increases  the  cost. 

From  the  above  it  is  seen  that  almost  all  conditions  incident  to 
the  building  of  a  bridge  on  a  curve  tend  to  increase  the  cost;  and 
hence  a  fundamental  principle  of  bridge  engineering:  Avoid  build- 
ing bridges  on  curves. 

63.  Weights  and  Loadings.  For  the  weight  of  steel  in  any 
particular  span,  and  for  the  loading  required  for  any  particular  class 
of  bridge,  see  Articles  20  to  23,  Part  I.  The  weight  of  the  ties  and 
the  rails  and  their  fastenings  is  usually  set  by  the  specifications  at 
400  pounds  per  linear  foot  of  track.  For  highway  bridges  the  weight 
of  the  wooden  floor  is  usually  taken  at  4^}  pounds  per  square  foot  of 
roadway  for  every  inch  in  thickness  of  floor. 

Highway  bridges  are  divided  into  different  classes  according  to 
their  loadings  (see  Cooper's  Specifications).  The  decision  as  to  the 
class  to  be  employed  depends  somewhat  upon  the  distance  to  the 
nearest  bridge  across  the  same  stream.  In  case  the  nearest  bridge 
is  only  a  few  miles  away  and  is  of  heavy  construction,  it  is  not  actually 
necessary  to  construct  a  heavy  bridge  at  the  proposed  site,  the  heavier 
traffic  being  required  to  pass  over  the  other  bridge.  In  case  a  heavy 
bridge  is  not  in  the  neighborhood,  then  one  should  be  constructed  at 
the  proposed  site.  If  the  proposed  site  is  on  a  road  connecting  adja- 
cent towns  of  large  size,  then  a  heavy  bridge  should  be  constructed 
and  provision  made  for  future  interurban  traffic,  even  if  none  is  at 
that  time  in  view,  since  it  will  be  more  economical  to  do  this  than  to 
erect  a  new  bridge  in  the  future. 


148 


K 


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140  BRIDGE  ENGINEERING 

In  the  case  of  railroad  Bridges,  new  ones  are  nearly  always  con- 
structed to  carry  the  heaviest  main  line  engines.  These  are  usually 
of  a  class  corresponding  to  Cooper's  E  40  or  E  50.  In  some  localities 
branch-line  bridges  are  built  for  the  same  live  loadings;  but  in  the 
majority  of  cases  the  branch-line  bridges  consist  of  the  old  bridges 
from  the  main  line. 

64.  Specifications.     For  any  particular  bridge   the  specifica- 
tions are  either  written  by  the  engineer  in  charge,  or  some  of  the  very 
excellent  general  specifications  which  are  on  the  market  in  printed 
form  are   used.     Some   railroads   use    these   general   specifications 
with  the  addition  of  certain   clauses  which  are  desired  by  the  chief 
or   bridge    engineer.     The    principal    differences    in    these    general 
specifications  are  in  regard  to  the  allowance  for  impact. 

Whenever  highway  design  is  mentioned  in  this  text,  it  is  to  be  in 
accordance  with  Cooper's  Highway  Specifications  (edition  of  1001). 
Wherever  plate-girder  design  is  given,  it  is  in  accordance  with  Cooper's 
Railway  Specifications  (edition  of  1906);  and  wherever  truss  design 
is  given,  it  is  in  accordance  with  the  general  specifications  of  the 
American  Railway  Engineering  &  Maintenance  of  Way  Association 
(second  edition,  1906). 

65.  Stress  Sheet.    Before  the  sections  are  designed,  the  com- 
puter makes  a  skeleton  outline  of  the  truss,  and  on  this  places  the 
dead-load  and   live-load  stresses,  and,  in  case  the  wind  should  be 
considered,  the  wind-load  stresses.  This  is  sent  to  the  designer.  The 
designer  determines  the  various  sections,  and  also  the  moments  and 
shears  in  the  stringers  and  floor-beams.     These  are  placed  on  a  sheet 
usually  17  by  23  inches.     This  is  called  a  stress  sheet.    This  sheet  is 
now  given  to  the  draftsman,  who  makes  a  shop  drawing.     The  stress 
sheets  for  railroad  bridges  are  usually  more  elaborate  than  those  for 
highway  bridges.     Plate  I  is  the  stress  sheet  of  a  highway  bridge; 
and  Plate  II  (Article  78)  and  Plate  III  (Article  93)  are  examples  of 
the  best  modern  practice  in  the  making  of  plate-girder  and  truss- 
bridge  stress  sheets. 

66.  Floor  System.    Perhaps  no  part  of  bridge  design  is  better 
standardized    than   the  construction   of   the  open   steel   floors   for 
railroad  bridges.     The  stringers  are  usually  placed  6  feet  6  inches 
apart,  and  consist  of  small  plate-girders,  or,  if  the  panel  length  is 
short,  of  one  or  more  I-beams.     I-beams  are  economical  in  regard  to 


150 


BRIDGE  ENGINEERING 


141 


TABLE  XIX 
Safe  Spans  for  I  Beams 

(Based  on  unit-stress  of  10  000  Ibs.  per  square  inch  in  extreme  fibre) 


fc,  Z 
o  < 

N^Q 

dS-i 

£8 

2^7 

£   K^ 

££6 

25 
30 
35 
30 
35 
40 
31% 
40 
50 
65 
42 
50 
60 
70 
80 
55 
65 
75 
80 
90 
65 
75 
85 
90 
100 
80 
85 
90 
95 
100 

MOMENT 

OF 

INERTIA 
1  1-Beam 

ENGINE  CLASS  E  40 

ENGINE  CLASS  E  50 

Safe  span  C  to  C  of  Bearings 

Safe  span  C  to  C  of  Bearings 

1  Beam 
per  rail 

2  Beams 
per  rail 

3  Beams 
per  rail 

1  Beam 
per  rail 

2  Beams 
per  rail 

3  Beams 
per  rail 

9  in. 
9  " 
9  " 
10  " 
10  " 
10  " 
12  " 
12  " 
12  " 
12  " 
15  " 
15  " 
15  " 
15  " 
15  " 
18  " 
18  " 
18  " 
18    ' 
18    « 
20    ' 
20    ' 
20    ' 
20    ' 
20    ' 
24    ' 
24  " 
24  " 
24  " 
24  " 

92 
102 
112 
135 
163 
175 
218 
274 
332 
403 
443 
515 
619 
718 
774 
809 
.890 
1023 
1  063 
1  188 
1  180 
1  277 
1  453 
1  502     ; 
1  650 
2112 
2182 
2356 
2427 
2497 

5  ft.  3  in. 
5  ••   9    " 

G  "    6    " 
6  "    9     ' 
8  "    6     ' 

7  ft.  9  in. 
8  "    9    " 
9  "    6   " 
10  "    0    " 
11  "    0    " 

4  ft.  9  in. 
5  ••   0   " 
5  "    3     ' 
5  "    9     ' 

7  "    0     ' 

7  ft.  0  in. 
7  "   0    " 

7  "    9    " 
8  "    6    " 
10  "    0    " 

3  ft'.  6  in.' 
4    '    3   " 
4    '    6    " 
4    '    9    " 
5    '    9    " 
7    '    3    " 

3  ft.  0  in. 
3  "    6   " 

9  "    3     ' 
11  "    6     ' 
12  "    6     ' 

12  "    9    " 
13  "    9    " 
15  "    3    ' 

4  ••    0    " 
4  "    9    " 
6  "    0    " 

7  "    9     ' 
9  "    6     ' 
11  "    3     « 

11  "    3    " 
12  "    3    " 
13  "    6    " 

8    '    6    " 

7    '    6    " 

12  "    9     ' 

15  "    6    ' 

6-3    " 

11  "    6     ' 

15  "    0    " 
14  "    0    " 

12    '    0    " 
11    '    0    " 
11    '    9    " 

K  "    3     ' 

21  "    6    ' 

10  "    9    " 

15  "    3     ' 

19  "    3    " 

16  "    0     ' 
16  "    9     ' 

20  "    9    " 

10  "    6    " 

15  "    0    " 

17  "    9    " 
18  "    9    " 
20  "    0    " 

12    '    6    " 
12    '    9    " 
13    '    6    " 
12    '    9    " 
13    '    3    - 
14    '    3    " 

19  "    6     ' 

18  "    9     ' 
19  "    6     ' 
21  "    0     ' 

24  "    6    " 
23  "    0    " 
24  "    0    " 

26  "    0    " 

12  "    3    " 
11  "    6    " 
12  "    0    " 

12  "    9    " 

17  "    6    " 
16  "    6    " 
17  "    3    " 
18  "    6    " 

21  "    9    " 
20  "    9    " 
21   "    3    " 
23  "    0    " 

14    '    6    " 

21  "    3     ' 

15    '    9    " 
16    '    0    " 
17    '    0    " 
17    '    3    " 
17    '    6    " 

23  "    0     ' 
23  "    9     ' 
24  "    6     ' 
25  "    0    " 
25  "    3    " 

29    '    3    " 
29    '    9    " 
30    '    9    " 
31    •    6    " 
32    '    0    " 

14  "    0    " 
14  "    6    " 
14  "    9    " 
15  "    0    " 
15  "    3    " 

20  "    6    " 
21  "    0    " 
21  "    6    " 
22  "    0    " 

22  "    6    " 

25  "    9    " 
26  "    3    " 
27  "    3    " 
27  "    9    " 
28  "    0    " 

DIAGRAM 

OF 

ENGINES 

g      §§§§      g   §    8   8 

§         §     o,     o     o          o     q      0     o 
o          o'     o      o'     o          o"     tD      \Q     <0 
ru         <J     t     *     ^          U     iu      ru     ru 

o  OOOO   oooo 

§°         oooo          oooo 
oooo         «n    m      "X    «o 

£      g  S  S   S?      S  Sf    S!   " 

o  OOOO   oooo 

-   8     -  S-  S-  5'-    9'    -  S-  6'  -  S- 

-  8'   -S'-S'-S'-    9'    -5'-  6'-  5'- 

first  cost,  but  are  disadvantageous  on  account  of  the  eccentric  con- 
nections which  necessitate  heavy  brackets  to  resist  part  of  their  re- 
action. They  are  also  somewhat  undesirable  on  account  of  the  fact 
that,  the  ties  deflecting,  most  of  the  load  is  carried  by  the  inner 
I-beam.  However,  I-beams  for  stringers  and  for  short-span  bridges 
(see  Fig.  121)  are  much  used  in  present  practice,  and  give  good  re- 
sults. Figs.  121  to  127  show  the  standard  open  floor  sections  of  the 
I^ehigh  Valley  Railroad.  Table  XIX  gives  the  required  number  of 
I-beams,  together  with  their  weight,  which  are  to  be  used  for  short- 
span  bridges  or  as  stringers  in  panels  of  given  length. 

Solid  floors  consist  of  angles  and  plates,  channels  and  plates,  or 
other  shapes.  They  extend  transversely  across  the  bridge  from  truss 


151 


142 


BRIDGE  ENGINEERING 


0'.,,"                                                                                                  .1 

to  truss,  the  lower 
chords,  in  case  of 
j      truss  bridges,  be- 

1£= 

1  r"              Hoi" 

JVl                        |  a'-V         "TL. 

t  p^^r^l-    8'*  9'"  10'  0   ^s>  =z=^-i^\±^p*^- 

T     ing    made    heavy 
enough   to  act  as 
girders  as  well  as 
tension  members. 
Figs.   128  to   130 
show   sections   of 
solid  floors.     The 
ballast  is  laid  di- 
^      rectly  upon  these 

4 

Fig.  121.    Sec 
Itailroac 
use 

r  ^r   r 

;tional  View  Showing  Open-Floor  Construction 
Bridge  of  Short  Span,  Single  Track.    I-Beams 
i  for  Stringers.    Lehigh  Valley  Standard. 

h                                           „  „                                          ., 
"H   h  j*0.£    1  •4''1*  .  18I"  }*- 

'^^_±8i.        I8i  ^y; 

f      solid  floors,  wrhich 
are    first    covered 
with  a  good  damp- 
proof  paint.    The 
floors  should  also 
be  supplied   with 
good  drainage  fa- 
cilities. 

er 

Concrete      is 
sometimes  laid  di- 

J 

Fig.  122.    Se 
and  Truss 

-                              G'C"                          ^ 

L-tion  of  Open-Floor  Construction  of  Deck-Gird 
Bridge,  Single  Track.     Lehigh  Valley  Standard 
Plate-Girders  used  for  Stringers. 

rectly  upon  the  steel  floor,  and  the  ballast  put  upon  this  concrete, 


Fig.  123.    Floor  Construction  of  a  Through-Girder  Bridge,  Single  Track. 
Lehigh  Valley  Standard. 


159 


BRIDGE  ENGINEERING 


145 


which  has  previously  had  a 
"layer  of  some  good  waterproof- 
ing applied  on  its  upper  sur- 
face. 

67.  Practical  Considera= 
tions.  The  possibilities  of  the 
rolling  mill  and  the  various 
shops  of  a  bridge  company, 
such  as  the  drafting  room, 
forge,  foundry,  templet  shop, 
assembling  shop,  and  riveting 
and  finishing  shop,  and  also 
the  shipping  and  erect'rg  facil- 
ities, should  be  well  known  in 
order  to  make  the  most  eco- 
nomical use  of  them.  This 
requisite  knowledge  comes 
only  from  experience.  The 
best  way  to  obtain  this  experi- 
ence without  being  actually 
employed  in  the  shops,  is  to  go 
into  the  shops  every  chance 
that  presents  itself,  keep  your 
eyes  and  ears  open,  and  ask  all 
the  questions  you  can.  The 
use  to  be  made  of  handbooks 
of  the  various  steel  manu- 
facturers is  given  in  Part  I 
of  "Steel  Construction,"  and 
should  be  thoroughly  studied 
before  going  further.  Some 
one  of  these  handbooks  is  in- 
dispensable to  persons  design- 
ing steel  structures.  That  of 
the  Carnegie  Steel  Company 
(edition  1903)  is  one  of  the 
best,  and  will  be  frequently 
referred  to  in  the  present  text. 


155 


146  BRIDGE  ENGINEERING 

Copies  may  be  procured  from  the  Carnegie  Steel  Company,  Frick 
Building,  Pittsburg,  Pa.  The  usual  price  to  students  is  50  cents, 
to  others  $2.00. 

DESIGN  OF  A  PLATE=GIRDER  RAILWAY-SPAN 

68.  The  Masonry  Plan.  In  some  cases  the  general  dimensions 
of  the  masonry  are  limited;  such  a  case,  for  example,  would  occur  in 
the  crossing  of  a  street  or  narrow  waterway.  Here  the  length  of  the 
span  and  the  distance  above  the  street  or  the  surface  of  the  water, 


Drain  Pipe  / 

Fig.  129.    Solid-Floor  Construction  of  Plates  and  Angles. 

are  the  limited  dimensions.  The  span  and  under-clearance  may  be 
unlimited,  as  in  the  case  of  a  country  stream  crossed  by  a  roadway 
which  is  a  considerable  distance  above  the  surface  of  the  water. 
The  term  unlimited  is  not  here  used  in  its  exact  meaning,  as  the  span 
in  this  case  is  really  limited  by  the  cost,  which  rapidly  increases  with 
the  length  of  the  span. 

In  some  cases,  as  when  the  engineer  is  in  a  bridge  office,  the 
masonry  plans  are  sent  in  by  the  railroad.  In  such  cases  many  of  the 
limited  dimensions  are  fixed.  The  most  usual  dimensions  to  be  fixed 
are  the  elevation  of  base  of  rail,  the  elevation  and  size  of  the  bridge 
seat,  and  the  length  of  the  span  under  coping.  These  limit  the 
depth  of  the  girder,  or  the  depth  of  the  floor  if  it  be  a  through 
girder,  and  also  limit  the  length  of  the  bearing  plates  at  the  end. 
Fig.  131,  the  masonry  plan  of  a  road  crossing,  shows  in  general  what 
can  be  expected.  All  the  dimensions  usually  fixed  are  given,  and  those 
marked  x  and?/ may  or  may  not  be,  but  x  should  never  be  less  than 
3  feet. 

69.  Determination  of  the  Class.  As  before  mentioned,  the 
deck  plate-girder  should  be  used  if  possible,  since  its  cost  is  less. 
There  are  some  cases,  however — such  as  track  elevation  in  cities  — 
where  the  additional  cost  required  to  elevate  the  track  so  as  to  use  a 


156 


BRIDGE  ENGINEERING  147 


deck  plate-girder  will  more  than  balance 
the  saving  in  its  favor.  In  such  cases  the 
through  plate-girder  is  used. 

The  case  whose  design  is  under  con- 
sideration will  be  taken  similar  to  that  of 
Fig.  131,  and  the  span  will  therefore  be  a 
deck  one. 

70.  Determination  of  the  Span,  Cen= 
ter  to  Center.  Fig.  132  shows  the  various 
spans — namely,  under  coping,  center  to  cen- 
ter of  end  bearings,  and  over  all.  The  span 
under  coping  is  that  span  from  under  cop- 
ing to  under  coping  lines  of  the  abutments, 
and  is  so  chosen  as  to  give  the  required  dis- 
tance between  the  abutments  at  their  base. 
The  span  center  to  center  is  equal  to  the 
span  under  coping  plus  the  length  of  one 
bearing  plate.  The  span  over  all  is  the 
extreme  length  of  the  girder.  The  length 
of  the  bearing  plate  is  influenced  by  the 
width  of  the  bridge  seat,  and  also  by  the 
maximum  reaction  of  the  girder.  The 
length  should  seldom  be  greater  than  18 
inches  and  never  greater  than  2  feet,  as 
the  deflection  of  the  girder  will  cause  a 
great  amount  of  the  weight  to  come  on  the 
inner  edge  of  the  bearing  plate  and  also  on 
the  masonry,  in  which  case  the  masonry  is 
liable  to  fail  at  that  point  and  the  bearing 
plates  are  over-stressed. 

Cast-steel  bearings  are  now  almost 
universally  used.  They  decrease  the  height 
of  the  masonry,  and  distribute  the  pressure 
more  evenly  and  for  a  greater  distance 
over  the  bridge  seat.  When  these  castings 
are  used,  the  bearing  area  between  them 
and  the  girder  may  be  made  quite  small, 
thus  doing  away  to  a  great  extent  with  the 


157 


148 


BRIDGE  ENGINEERING 


deteriorating  effect  due  to  the  deflection  of  the  girder  as  mentioned 
aboVe.  Fig.  133  shows  the  end  of  a  girder  equipped  with  a  cast- 
steel  pedestal.  Table  XX  gives  the  length  of  the  bearing  on  the 


I/Center  Line  ot  Rood 
Under    Clearance  Line? 


|  * 6P-0' 


Elevation  7SfeOx.| 


Fig.  131.    Masonry  Plan  of  a  Road  Crossing. 

masonry  for  various  spans,  Cooper's  E  '40  loading  being  used  and 
cast-steel  pedestals  being  employed. 

TABLE    XX 
Length  of  Masonry   Bearings 


SPAN                                                               LENGTH  OF  BEARING 

1.5  to     24  ft 

r                                                    12  inches 

25  to    44 

16 

' 

•45  to    69 

21 

1 

70  to    79 

2.3 

« 

SO  to    89 

29 

' 

90  to  115 

36 

As  an  example,  let  it  be  required  to  determine  the  span  center 
to  center  of  a  deck  plate-girder  of  00-foot  span  under  coping,  the 


I 

i 

L 

j^  Masonry  Plate                                                                                             M 
r                                                       Span  Under   Copinq 

Bearmq  Area  —  J 
ionry  Bearing  ^p^ 

i 

i 

A                                                  Span    Center  to  Center   Bearmq                                                    ^ 

Fig.  132.     Diagram  Showing  Various  Spans  Considered  in  Bridge  Construction. 

loading  being  E  40.     From  Table  XX  it  is  seen  that  the  length  of 
the  masonry  l>earing  will  l>e  21  inches,  and  therefore  the  span  center 


158 


BRIDGE  ENGINEERING 


149 


to  center  of  bearings  will  be   60  +  2  X  (I  X  1  ft.  9  in.)  -  61  feet 
9  inches. 

In  Articles  71  to  77  the  above  girder  will  be  designed ;  and  also 
such  information  as  is  of  importance  regarding  the  subject-matter 
of  each  article  will  be  treated.  The  dead-  and  live-load  shears  are 
computed  by  the  methods  of  Part  I,  and  are  given  in  Fig.  134. 

71.  Ties  and  Guard=Rails.  The  length  of  ties  for  single-track 
bridges  is  10  feet. 
For  double-track 
bridges  the 
length  is  in  most 
cases  the  same. 
In  some  double- 
track  bridges, 
however,  either 
each  tie  or  every 
third  tie  extends 
entirely  across 
the  bridge.  In 
other  cases  every 
third  tie  on  one 
track  extends  to 
the  opposite 
track,  thus  act- 
ing as  a  support 
for  the  foot- walk 
which  is  laid 
upon  them.  It 
is  the  best  prac- 
tice to  limit  the  length  of  the  ties  on  double-track  bridges  to  10  feet, 
since,  if  they  extend  into  the  opposite  track  in  any  way  whatsoever, 
unnecessary  expense  is  incurred  whenever  repairs  or  renewals  are 
made,  because  both  tracks  must  necessarily  be  disturbed  to  some 
extent. 

The  size  of  the  ties  varies  with  the  weight  of  the  engines  and  the 
spacing  of  the  stringers  or  girders  on  which  they  rest.  They  are 
usually  sawed  to  size  instead  of  hewn,  and  the  following  sizes  may  be 
purchased  on  the  open  market — namely,  6  by  8,  7  by  9, 8  by  9,  9  by  10, 


a 

=5 

rr^rr 

"-•^A 

/ 

i 

\  "-1 

'//^////^////////, 

f  , 

Section    A-A 


Span  Undtr    Coping 
5paa  Center  to  Center 


Span    Over  AU 


Fig.  133.    End  of  a  Girder  Equipped  with  a  Cast-Steel  Pedestal. 


lit 


150 


BRIDGE  ENGINEERING 


1600 


300 


Fig.  134.    Shear  arid  Moment  Diagram. 


160 


BRIDGE  ENGINEERING  151 

and  10  by  12  inches.     Larger  sizes  may  be  obtained  on  special  order. 

The  elevation  blocks  (see  Fig.  127)  should  be  of  length  to  suit  the 
width  of  the  cover-plates  and  the  spacing  of  the  supports.  They  are 
usually  made  of  the  best  quality  of  white  oak,  since  the  cost  of  renewal 
is  great  enough  to  demand  that  they  be  made  of  material  as  permanent 
as  possible. 

The  guard-rails  should  be  placed  in  accordance  with  the  specifica- 
tions (see  Articles  13  and  14).  Some  railroads  specify  that  the  guard- 
rails shall  be  in  24-foot  lengths  unless  the  bridge  is  shorter  than  24 
feet,  in  which  case  one  length  of  timber  should  be  used.  For  method 
of  connection  and  other  details,  consult  Figs.  121  to  127.  The 
guard-rails  and  the  ties  are  usually  made  of  Georgia  long-leaf  yellow 
pine,  prime  inspection.  Other  wood,  such  as  chestnut,  cedar,  and 
oak,  may  be  used. 

In  addition  to  the  wooden  guard-rail,  a  steel  guard-rail  usually 
consisting  of  railroad  rails  is  placed  within  about  8  inches  of  the 
track  rail. 

In  designing  ties,  the  problem  is  that  of  a  simple  beam  symmet- 
rically loaded  with  two  equal  concentrated  loads,  the  weight  of   the 
rail  and  tie  itself  usually  being 
neglected.  For  the  case  in  hand, 

which  is  that  of  a  deck  plate-  A -^ J^j 

girder,   loading  E  40,  the  con-      t^--^^^—--^-.^^----^  ^J — —  i 
centra  ted  load  for  which  the  tie      ^^-^        '""^ 
must  be  designed  is,  according  Rr 

to  Specifications  (Article  23,  3d 

r»ai-^  Q  Q'*'}  T\r>nnr1o  A «« rvr-rl i n ,  Fig.  135.  Distribution  of  Loading  on  Ties  Of 
part),  S  666  pounds.  According  Deck  plate-Girder  Bridge. 

to  Article  23,  100  000  pounds  is 

on  four  wheels.  This  gives  25  000  pounds  on  one  wheel,  and  ac- 
eording  to  Article  15,  one-third  of  this,  or  8  333  pounds,  will  come 
on  one  tie.  Fig.  135  shows  the  condition  of  the  loading,  the  space 
center  to  center  of  rail  being  taken  as  4  feet  10  inches.  Some 
designers  take  this  distance  as  5  feet;  but  as  the  standard  rail  head 
is  about  2  inches,  and  the  standard  gauge  4  feet  8^  inches,  the  distance 
here  taken  seems  to  be  the  more  logical  one. 

The  formula  to  be  used  in  the  design  of  this  beam  is  that  given 

OT 

in  "Strength  of  Materials,"  and  is  M  =  —  In  this  case  M=10  X 


161 


i_J. 

r 


BRIDGE  ENGINEERING 


and  c  =  d  -r-  2,  and  therefore  -  = 

c         6 


8  333  =  83  330  pound-inches.     In  the  above  formula,  7  =  W-^  12, 

Substituting    the    value 

of  the  moment  in  the  above  formula, and  solving  for  S,  there  results' 

499  980 
bda 

For  a  6  bv  8-inch  tie,  the  unit-stress  would  then  be : 


S  =  - 


=  1  310  pounds. 


If  a  7  by  9-inch  tie  is  used,  the  unit-stress  is  found  to  be  880  pounds. 

Since  according  to  Article  15  of  the  Specifications,  the  unit-stress 

cannot  be  greater  than  1  000  per 
square  inch,  it  is  necessary  to  use 
a  7  by  9-inch  tie.  If  the  engine 
loading  had  been  E  50,  the  mo- 
ment would  have  been  100000 
pound-inches,  and  then  the  stress 
in  a  7  by  9-inch  tie  would  be  1  0(>0 
pounds  per  square  inch,  and  the 
stress  in  an  8  by  9-inch  tie  would 
be  930  pounds,  which  would  neces- 
sitate the  use  of  the  latter. 

The  guard-rails  on  this  bridge 
will  be  placed  according  to  the 
Lehigh  Valley  standard,  and  hence 
their  inner  face  will  be  4  feet  1^ 
inches  from  the  center  of  the 
track. 

Elevation    blocks    will    not    be 
required,  as    the    bridge   is  on  a 
tangent. 
72.     The  Web.    The  economic  depth  of  the  web,  according  to 

Article  59,  Part  I,  will  be: 


Fig.  136.    End  Rivets  Transferring  Shear 
to  Web. 


Cl  ft.  9  in. 

Depth  = 


0.543 


rs  =  72.5. 


The  depth  might  be  taken  as  72  inches,  but  74  inches  will  be  decided 
upon,  as  this  will  decrease  the  area  of  the  flange  and  also  will  not 
affect  the  total  weight  to  any  great  extent-  The  unit-stress  for  shear 


169 


BRIDGE  ENGINEERING 


153 


Is  9  000  pounds  per  square  inch  (see 
Specifications,  Articles  40  and  41). 

The  maximum  shear  in  the  girder 
occurs  at  the  end,  where  it  is  117  800 
pounds.  The  area  required  for  the  web 
is  then  117  800  -f-  9000  -  13.09  square 
inches,  and  the  required  thickness  is  13.09 
-r-  74  =  0.177  inch.  This  latter  value 
cannot  be  used,  since,  on  account  of  Ar- 
ticle 82  of  the  Specifications,  no  material 
less  than  f  inch  can  be  used.  The  web 
plate  will  therefore  be  taken  as  74  in.  by 
|  in.  in  size. 

Some  engineers  insist  that  the  net 
section  of  the  web  should  be  considered. 
Consider  Fig.  136,  the  shear  being  trans- 
ferred to  the  web  by  the  end  rivets.  The 
web  will  not  tend  to  shear  along  the 
section  B-B,  in  which  case  the  rivet-holes 
should  be  subtracted;  but  it  will  shear 
along  section  A- A,  a  section  which  is 
unaffected  by  the  rivet-holes.  The  web 
splice  should  come  at  one  of  the  stiffeners, 
and  will  therefore  be  considered  in  Arti- 
cle 76. 

73.  The  Flanges.  This  portion  of 
the  girder  is  usually  built  either  of  two 
angles  or  of  two  angles  and  one  or  more 
plates.  In  heavy  girders  where  the  flange 
areas  are  large,  additional  area  is  OD- 
tained  by  using  side  plates  or  side  plates 
and  four  angles.  Sometimes  two  chan- 
nels are  used  in  the  place  of  side  plates 
and  angles.  Fig.  137  shows  the  different 
methods  of  constructing  the  top  flanges 
of  girders.  The  lower  flanges  are  usually 
of  the  same  construction.  Fig.  137  b  has 
the  web  extending  beyond  the  upper  sur- 


163 


154 


BRIDGE  ENGINEERING 


faces  of  the  upper  flange  angles.  This  is  done  in  order  that  the 
ties  may  be  dapped  over  it,  and  thus  prevent  the  labor  usually 
required  for  cutting  holes  in  the  lower  face  of  the  tie  in  order  to 
allow  for  the  projecting  rivet-heads.  Fig.  137  g  is  usually  uneconom- 
ical, since  the  thinness  of  the  channel  web  requires  a  great  many 
rivets  to  sufficiently  transmit  the  shear  from  the  web  to  the  flange, 
and  also  since  the  cover-plates  must  be  very  narrow. 

Specifications  usually  state  that  the  flanges  shall  Have  at  least 
one-half  of  the  total  flange  area  in  the  angles,  or  that  the  angles  shall 
be  the  largest  that  are  manufactured.  The  largest  angles  are  not 
usually  employed,  since  their  thickness  is  greater  than  three-quarters 
of  an  inch  and  therefore  the  rivet-holes  must  be  bored,  not  punched. 
The  reason  for  this  is  that  the  depth  of  the  rivet-hole  is  too  great  in 
proportion  to  its  diameter,  and  on  this  account  the  dies  used  for 
punching  frequently  break.  Also,  the  punching  of  such  thick  material 

injures  the  adjacent  metal,  which 
makes  it  undesirable.  In  reality 
the  flange  area  of  only  the  short- 
span  girders  is  small  enough  to 
allow  the  flange  area  to  be  taken  up 
by  the  angles. 

In  choosing  the  thickness  of  the 
cover-plates,  care  should  be  taken 
so  that  the  outer  row  of  rivets  will 
not  come  closer  to  the  outer  edge 
of  the  plate  than  eight  times  the 
thickness  of  the  thinnest  plate.  In 


at  orkss 
not  over  5"   c3Qt  or  less. 


Fig.  138.    Diagram  Showing  Relation  be- 
tween Thickness  of  Coyer-Plates 
and  Position  of  Rivets. 


case  eight  times  the  thickness  of  the  plate  is  greater  than  5  inches, 
then  5  inches  should  be  the  limit.  Also,  the  distance  between  the 
inner  rows  of  rivets  should  not  exceed  thirty  times  the  thickness  of 
the  thinnest  plate.  These  limitations  are  placed  by  Article  77  of  the 
Specifications,  and  Fig.  138  indicates  their  significance. 

The  determination  of  the  required  flange  area  depends  upon  the 
distance  between  the  centers  of  gravity  of  the  flanges;  and  in  order 
to  determine  this  exactly,  the  area  and  composition  of  the  flanges 
should  be  known.  The  above  condition  requires  an  approximate 
design  to  be  made,  the  supposition  being  that  the  flanges  consist  of 
two  angles  and  one  or  more  plates  as  shown  in  Fig.  138. 


164 


BRIDGE  ENGINEERING  155 

The  distance  back  to  back  of  angles  will  be  taken  as  74  +  2  X 
|  =  74^  inches.  Article  74  of  the  Specifications  requires  ^  inch; 
but  I  ;  inch  is  better  practice,  since  the  edges  of  the  web  plate  are  very 
liable  to  overrun  more  than  -^  inch.  Some  specifications  require 
3-  inch. 

In  the  computation  of  the  approximate  flange  area,  the  center 
of  gravity  of  each  flange  will  be  assumed  as  one  inch  from  the  back 
of  the  angles.  The  approximate  effective  depth  is  then  74j  less  2 
X  1  inch,  which  equals  72  j  inches.  The  approximate  stresses  in 
the  flange  areas  are  : 

,  275  000  x  12 
I  or  dead  load,  -          -     =  4o  GOO  pounds. 


For  live  load,]  .  12.  -  222000  pounds. 


The  approximate  flange  areas  are  now  obtained  by  dividing 
these  amounts  by  the  allowable  unit-stresses  for  dead  and  live  load, 
which  are  (see  Specifications,  p.  8,  Article  31):  20  000  and  10000 
pounds  per  square  inch  respectively;  and  the  resulting  areas  are: 

For  dead  load,  -  -- --         =  2 . 28  square  inches. 
For  live  load,  =  22. 20 square  inches. 

These  amounts  give  a  total  of  24.48  square  inches  as  the  approximate 
net  flange  area  required. 

It  will  be  assumed  that  one-half  the  total  area,  or  24.48  -r-  2  = 
12.24  square  inches,  is  to  be  taken  up  by  angles.  If  12.24  sq.  in. 
is  distributed* over  two  angles,  then  12.24  -7-2  =  6.12  square  inches 
is  the  net  area  for  one  angle.  Of  course  it  is  not  to  be  assumed  that 
the  area  of  the  angle  chosen  must  be  exactly  6. 12,  but  that  this  6. 12 
square  inches  is  the  approximate  area  of  the  angle  to  be  chosen,  and 
the  net  area  of  the  angle  (see  Specifications,  Article  149)  must  not  be 
2  j  per  cent  less  than  this,  although  it  may  be  greater. 

From  Steel  Construction,  Part  I,  Table  VII,  or  from  the  Car- 
negie Handbook,  p.  117,  a  6  by  6  by  f-inch  angle  gives  a  gross  area  of 
8.44  square  inches  and  a  net  area  of  8.44  -  2  X  (f  +  |)  X  f  = 
6 . 94  square  inches,  f-inch  rivets  being  used  and  so  spaced  that  two 
rivets  are  taken  out  of  each  angle  (see  Specifications,  Article  63, 
and  Fig.  139).  A  6  by  4  by -j  f-inch  angle,  giving  a  gross  area  of 
7.47  and  a  net  area  of  6.66  square  inches,  one  rivet-hole  being  out> 


105 


150 


BRIDGE  ENGINEERING 


Fig.  139.    Calculation  of  Size  of  Angle 
and  Cover-Plate. 


could  have  boon  used,  but  { e  inch  is  too  thick  to  punch,  and  there- 
fore the  above  angle  is  chosen. 

The  required  net  area  of  the  cover-plate  is  now  found  to  be 
24.48  -  2  X  6.94  =  10. 60  square  inches.  Since  the  legs  of  the 
angles  are  6  inches  and  the  thickness  of  the  web  is  |  inch,  the  outer 

edges  of  the  angles  are  12f  inches 
apart;  and  since  the  cover-plate 
must  extend  somewhat  over  the 
edges  of  the  angle,  and  the  width 
of  the  cover-plate  should  be  in  the 
even  inch,  the  width  of  the  cover- 
plates  must  be  at  least  14  inches, 
as  shown  in  Fig.  139. 

On  account  of  the  1-inch  rivet- 
holes  to  be  deducted,  the  real  or 

net   width   of   the   cover-plate  '  is:   2  X  n  +  m  =  14  —  2  X  1  =  12 
inches.     The  thickness  of  all  the  cover-plates  at  the  center  is  now: 

10   Cii) 
t  =  —  r>-  -  =  O.SS5  inch— say,  Jjj  inch. 

A  thickness  of  I  of  an  inch  is  decided  upon,  for  the  reason  that  plates 
are  rolled  only  to  the  nearest  sixteenth  of  an  inch. 

The  approximate  section  at  the  center  has  now  been  determined, 
and  is: 

2  Angles  (i  by  <>  hy  ^-inch  =   1I5.8S  sq.  in.  net. 
Cover-plates  I  inch  thick    =  lO.oOsq.  in.  net. 

Total    =  24.38  sq.  in.  net. 

This  approximate  section  must  now  be  examined,  and,  if  it  shows  too 
great  an  excess  or  a  de- 
ficiency, must  be  revised. 
In  order  to  deter- 
mine  the  effective  depth 
the  distance  between  the 
centers  of  gravity  of  the 
flanges  must  first  be  com- 
puted, the  gross  areas  be- 
ing used.  Theoretically,  perhaps,  the  net  areas  should  be  used; 
but  this  is  an  unnecessary  refinement,  since  the  effect  on  the  final 
result  is  of  no  practical  importance. 


0.875" 


Fig.  140.    Determination  of  Center  of  Gravity. 


166 


BRIDGE  ENGINEERING  157 


In  computing  the  center  of  gravity  (see  Fig.  140),  the  axis  is 
taken  at  the  center  of  the  cover-plates,  as  this  reduces  the  moment  of 
the  cover-plates  to  zero.  The  distance  of  the  center  of  gravity  of  the 
angles  from  their  back  (Carnegie  Handbook,  p.  117,  column  6)  is 
1 .78  inches.  The  distance  of  this  center  of  gravity  from  the  center 
of  the  cover-plate,  is  1 .78  +  0.875  -^  2  =  2.22  inches. 

Gross  aceaof  the  angles  =  2  X  8.44        =10.88  sq.  in. 
"   cover-plates  =  I  X  14  =  12.25  sq.  in. 

Total  =   29.13  sq.  in. 

The  center  of  gravity  is  now  found  to  be  10.88  X  2.22  -=-  29.13  = 
1.286  inches  from  the  center  of  the  cover-plate,  and  1.286-0.875 
-=-2=0:848  inch  from  the  back  of  the  angle.  The  effective  depth 
he  is  74.25  -  2  X  0.848  =  72.554  inches,  and  the  required  flange 
areas  are: 

275  000  X  12 


72 . 554  X  20  000 

1  340  OOP  X  12 

"727554  X  10  000 


=     2.272  sq.  in.  for  dead  load. 
=  22.200  sq.  in.  for  live  load. 


Total  =  24.472  sq.  in. 

The  values  of  the  moments,  as  taken  from  the  curves,  must  be  mul- 
tiplied by  12  in  order  to  reduce  them  to  pound-inches. 

A  total  of  24.86  square  inches  is  given  by  the  section  approxi- 
mately designed,  and  the  difference  between  that  and  the  section  as 
above  determined  is :  (24 . 472  -  24 . 38)  -r-  24 . 472  =  0 . 38  per  cent, 
and  as  this  is  less  than  2^  per  cent  (see  Specifications,  Article  149),  it 
may  be  used  without  any  further  change.  If  there  should  have  been 
a  deficiency  or  an  excess  greater  than  1\  per  cent,  then  it  would  have 
been  necessary  to  revise.  In  case  a  revision  of  section  is  necessary,  the 
size  and  thickness  of  the  angles  generally  remain  the  same  as  those 
taken  in  the  approximate  design,  the  thickness  of  the  cover-plates 
being  decreased  or  increased  as  the  case  may  be. 

The  total  thickness  of  the  cover-plates,  -£  inch,  is  too  thick  to  be 
punched.  In  such  cases  as  this,  the  section  is  made  up  of  two  or  more 
plates  whose  total  thickness  is  equal  to  that  required.  If  plates  of 
more  than  one  thickness  are  decided  upon,  then  their  thickness 
should  decrease  from  the  flange  angles,  outward.  For  the  case  in 
hand,  one  plate  \  inch  thick  and  one  plate  \  mcn  thick  will  be  decided 
upon.  The  flange  section  at  the  center  as  finally  designed  is: 


167 


158 


BRIDGE  ENGINEERING 


SHAPE 

NET  SECTION               GROSS  SECTION 

2  Angles  6  by   6  by 
1  Cover-plate  14  by 
1  Cover-plate  14  by 

fin. 
fin. 
Jin. 

13.88  sq.  in. 
4  .  50     '  ' 
6  .  00     " 

16.88  sq.  in. 
5  .25     " 
7.00     " 

Total 

24.  38     '  ' 

29.13     " 

The  above  is  the  section  required  at  the  center  of  the  girder; 
for  any  other  point  it  will  be  less,  decreasing  toward  the  end,  where 
it  will  be  zero.  Evidently,  then,  the  cover-plates  will  not  be  required 
to  extend  the  entire  length.  The  following  analysis  will  determine 
where  they  should  be  stopped.  If  the  load  were  uniform,  the  moment 


Fig.  141.    Diagram  Showing  Curve  of  Required  Flange  Areas. 

curve  would  be  a  parabola.  Although  under  wheel  loading  the  curve 
of  moments  is  not  a  parabola,  yet  it  is  sufficient  for  practical  purposes 
to  consider  it  as  such.  The  curve  of  flange  areas,  like  that  of  moments, 
is  to  be  considered  a  parabola  (see  Fig.  141). 

Let  «j  =  Net  area,  in  square  inches,  of  the  outer  cover-  plate; 

a.,  =  Net  area,  in  square  inches,  of  the  next  cover-plate; 

(ix,  etc.  =  Net  areas  of  the  other  cover-plates; 

A  =  Net  area  of  all  the  cover-plates  and  the  flange  angle. 
Then,  from  the  properties  of  the  parabola, 


where  L  =  Length  of  cover-plate  in  question; 
I  =  Length  of  span,  center  to  center; 
a  =  Net  area  of  that  cover-plate  and  all  above  it;  and 
A  =  Total  net  area  of  the  flange,  $  of  the  gross  area  of  the  web  not  being 
considered  in  this  quantity. 


168 


BRIDGE  ENGINEERING  150 


The  lengths  of  the  cover-plates  for  the  section  above  designed  (see  Fig.  141) 
are: 


L,  -  61.75  -        -        =  26.45  feet. 


Lo  =  61.75  J  -    ^p     =  40.00  feet. 
\  J4.OS 

One  foot  is  usually  added  on  each  end  of  the  cover-plate  as  theoretically 
determined  above.  The  results  are  also  usually  rounded  off  to  the  nearest 
half-foot.  This  is  done  in  order  to  allow  a  safe  margin  because  of  the  fact 
that  the  curve  of  flange  areas  is  not  a  true  parabola.  The  final  measurements 
of  the  cover-plates  are: 

14  in.  by  f  in.  by  28  ft.  6  in.  long. 

14  in.  by  £  in.  by  42  ft.  6  in.  long. 

In  most  cases  the  cover-plate  next  to  the  angle  on  the  top  flange  only  is 
made  to  extend  the  entire  length  of  the  girder.  Although  this  is  not  required 
for  flange  area,  it  is  done  in  order  to  provide  additional  stiffness  to  the  flange 
angles  toward  the  ends  of  the  span,  and  to  prevent  the  action  of  the  elements 
from  deteriorating  the  angles  and  the  web  by  attacking  the  joint  at  the  top 
(see  broken  lines,  Fig.  141,  for  length  of  first  cover-plate  extended). 

EXAMPLES  FOR   PRACTICE 

1.  The  dead-load  moment  equals  469  000  pound-inches;  and  the  live- 
load   moment,   4  522  000  pound-inches.       Design   a  flange  section  entirely 
of  angles,  if  the  distance  back  to  back  of  angles  is  45£  inches. 

2.  The  dead-load  moment  is  3  340  000  pound-inches,  and  the*  live- 
load  moment,  21  235  000  pound-inches.      Design  a  flange  section  using  6  by 
6-inch  angles  and  three  14-inch   cover- plates,  the  distance  back  to  back  of 
flange  angles  being  78}  inches. 

3.  In  each  of  the  above  cases,  design  the  flange  section   considering 
that  i  of  the  web  area  is  taken  as  effective  flange  area.     (For  demonstra- 
tion of  the  methods  to  be  employed  in  the  solution  of  this  problem,  see  the 
succeeding  text.) 

While  the  section  of  a  plate-girder  is  composite — that  is,  it  con- 
sists of  certain  shapes  joined  together,  and  is  not  one  solid  piece- 
nevertheless  these  shapes  are  joined  so  securely  that  the  section  may 
be  considered  as  a  solid  one  and  its  moment  of  resistance  computed 
accordingly.  Let  Fig.  142  be  considered. 

The  moment  of  resistance  of  the  section  is: 


in  the  derivation  of  which  the  moment  of  inertia  of  the  flange  about 
its  own  neutral  axis  is  considered  as  zero,  and  A  equals  the  net  area  of 
one  flange.  Now,  as  the  values  of  he  and  h  seldom  differ  by  more 


169 


160 


BRIDGE  EX( ]  IX EE  H ING 


than  one  inch,  for  all  practical  purposes  they  may  be  considered*  as 
equal.     The  above  expression  then  reduces  to: 

M  =  S  X  h(A   +  -  ~  ) 

=  S  X  h  (net  area  of  flange  +  one-sixth  gross  area  of  web) 
Since  the  rivet-holes  decrease  the  moment  of  resistance  of  the 
web,  one-sixth  of  the  gross  area  cannot  be  considered,  as  is  theoreti- 
cally indicated  in  the  above  formu- 
la.    It  is  common  practice  to  take 
one-eighth,  instead  of  one-sixth,  of 
the  gross  web  area.     Substituting 
this  value  in  the  above   equation, 
and  transposing,  there  results: 

Area  of  flange  -f  -J-  gross  web  area  =  ^.-  • 

O/l 

The  flange  section  will  now  be 
designed  for  the  moments  previously 
given,  considering  £  of  the  gross  web 
area  as  efficient  in  withstanding  the 
moment. 

The  gross  area  of  the  web  is 
74  x  |  =  27 . 75  square  inches ;  and 
|  of  this  is  3.47  square-inches.  The 
total  approximate  amount  of  flange 
area  required  is,  as  in  the  first  case, 
24.48  square  inches. 

According  to  the  above  formula, 
|  of  the  web  area,  or  3.47  square 
inches,  may  be  considered  as  flange 
area,  and  therefore  24.48  —  3.47  = 
21.01  square  inches,  is  the  approxi- 
mate area  of  the  angles  and  cover-plates  of  the  flange.  The  ap- 
proximate area  of  one  angle  is  then  21 ,01  -^  (2  X  2)  =  5.25  square 
inches.  A  6  by  6  by  f%-inch  angle  gives  the  gross  area  of  6.43  square 
inches  and,  two  rivet-holes  being  deducted,  a  net  area  of  5.305 
square  inches  (see  "Steel  Construction,"  Part  I,  Table  VIII,  or 
Carnegie  Handbook,  p.  117).  As  this  is  quite  close  to  the  approxi- 
mate area  determined  above,  this  angle  will  be  taken.  The  ap- 


Fig.  142.    Section  of  Plate-Girder. 


170 


BRIDGE  ENGINEERING 


101 


proximate  area  of  the  cover-plates  is  21.01  —  2  X  5.305  =  10.40 
square  inches.     As  before,  the  gross  width  of  the  cover-plate  will 

10.40 


be   taken  as    14   inches. 


The    thickness    is   then  — - 

14       £  (-, 


=  0.867  inch — say  f  inch. 

The  gross  area  of  the  angles  being  12.86  square  inches,  and  that 
of  the  cover-plates  12.25  square  inches,  the  center  of  gravity  of  the 
section  is  found,  by  a  method  similar  to  that  previously  employed, 
to  be  1 .10  inches  from  the  center  of  the  cover-plate,  or  1.10  —  0.438 
=  0 . 662  inch  from  the  back  of  the  flange  angles.  This  makes  the 
effective  depth  72.93  inches. 

For  this  section,  the  true  live-load  flange  stress  is  (1  340  000  X 
12)  -=-  72 . 93  =  221 000  pounds,  and  the  actual  dead-load  flange  stress 
is  (275000  X  12)  -=-  72.93  =  45400  pounds.  The  actual  areas 
required  for  the  live  and  dead  load  are  22. 10  and  2.27  square  inches, 
which  are  obtained  by  dividing  the  above  flange  stresses  by  10  000 
and  20  000  pounds,  respectively.  The  total  required  area  is  the  sum 
of  the  twro  areas  above,  and  is  equal  to  24.37  square  inches.  The 
total  area  required  in  the  flange  angles  and  cover-plates  is  therefore 
24.37,  less  -£  the  gross  area  of  the  web,  3.47,  which  leaves  20.90 
square  inches.  The  same  angles  as  decided  upon  before  will  be  used. 
This  gives  a  required  area  for  the  cover-plates  of  20.90  —  10.61  = 
10.29  square  inches.  The  required  thickness  is  then  10.29  -T-  (14 
—  2)  =  0.857 — say  £  inch.  The  following  section  of  the  flange  will 
therefore  be  decided  upon: 


SHAP 

E 

NET  SECTION 

GROSS  SECTION 

2  Angles  6  in.  by  6 
1  Cover-plate  14  in 
1  Cover-plate  14  in 

in.  by  T9ff  in. 
.  by  f  in. 
.  by  £  in. 

10.  Gl  sq.  in. 
4  .  50     '  ' 
6.00     " 

12.86  sq.  in. 
5.25     " 
7.00     " 

Total  = 

21.11     " 

25.11     " 

As  the  total  net  area  above  is  within  1\  per  cent  of  the  required  net 
area,  that  section  will  be  taken  (see  Specifications,  Article  149).  Note 
that  in  this  case,  the  thickness  of  the  cover-plates  in  the  final  design 
is  the  same  as  that  determined  in  the  preliminary  design. 
Also  note  that  the  total  net  area  is  about  4  square  inches,  or  20  per 


171 


162 


BRIDGE  ENGINEERING 


cent,  less  than  in  the  flange  as  first  designed,  in  which  case  none  of  the 
area  of  the  web  was  considered  as  withstanding  the  bending  moment. 
The  4-inch  cover-plate  on  the  top  flange  will  extend  the  entire 
length  of  the  grider,  and  is  therefore  62  feet  9  inches  long.  The 
lengths  of  the  other  cover-plates  are: 

For  Wnch  plate  at  the  bottom,  L  =  Gl  .7.5  -y  21'  11  =  4'?  '  5  fe<?t' 


For  each  f-inch  plate,  L  =  61.75  \  .^TT  =  28-5  feet- 

One  foot  should  be  added  to  each  of  the  above  lengths  at  each  end, 
thus  making  the  total  lengths  45  feet  (3  inches  and  30  feet  6  inches, 
respectively. 

EXAMPLES   FOR   PRACTICE 

1.  If  the  span  is  63  feet  center  to  center,  compute  the  length  of  the 
cover-  plate.     The  section  consists  of  two  angles  6  by  6  by  jj-  in.;  one  cover- 
plate  14  by  £  in.;  and  one  cover-plate  14  by  %  in.;  two  rivet-holes  being  taken 
out  of  each  angle  and  each  cover-plate. 

2.  If  the  span  is  87  ft.  9  in.  center  to  center,  compute  the  length  of  the 
cover-plate  if  the  flange  consists  of  two  angles  6  by  6  by  |  in.,  and  four  cover- 
plates  16  by  j9^  in.,  two  rivet-holes  being  taken  out  of   each  angle  and  each 
cover-plate. 

In  determining    the  area  of  plates,  the  tables  in  the  Carnegie 
Handbook,  pp.  245  to  250,  are  convenient.     In  order  to  obtain  plates 


T 

IA 

F     b 

o    - 

-6    ' 

•6    ' 

F                    F       c 

-0     'rO  j  ' 

6 

A 

. 

r 

•O          r 
F     b 

o    ', 

•9   ' 

o   'l-o  i  ' 

F                   F       £ 

O 

Fig.  1J3.    Diagram  Illustrating  Transference  of  Shear  from  Web  to  Flanges  by  Rivets. 

whose  widths  are  greater  than  12f  inches,  see  the  note  in  the  right- 
hand  column  on  page  250,  Carnegie  Handbook.  For  another  pres- 
entation of  the  above  subject-matter,  see  "Steel  Construction,"  Part 
IV.  pp.  252,  254,  and  261. 

The  spacing  of  the  rivets  in  the  flanges  is  a  matter  of  considerable 
importance;  the  shear  is  transferred  from  the  web  to  the  flanges, 
where  it  becomes  flange  stress.  This  is  done  by  the  rivets,  each  rivet 
taking  as  much  flange  stress  as  is  allowed  by  the  Specifications.  The 
conditions  are  similar  to  those  shown  in  Fig.  143,  where  V  represents 


178 


BRIDGE  ENGINEERING 


163 


an  object  exerting  a  pull  on  a  long,  thin  plate  A  -  A  which  has,  at 
various  points  along  this  length,  small  objects  F  attached  to  it  by 
means  of  pegs  r-r.  These  smaJl  objects  F  hold  the  plate  A-  A  in 
equilibrium.  Here  V  represents  the  shear  which  tends  to  cause  the 
movement;  A  -A,  the  web;  r-r,  the  rivets;  and  2F  the  amount  of 
flange  stress  taken  by  each  rivet. 

At  section  c  -  c  the  total  amount  in  the  web  to  be  trans- 
formed is  2F;  at  section  6-6 
it  is  10F.  From  this  it  is  seen 
that  enough  rivets  r-r  must  be 
put  in  between  the  sections  6  - 
6  and  c  -  c  to  take  up  10F  - 
2F  =  8F;  hence  it  is  proved 
that  the  rivets  between  any  two 
sections  of  the  flange  take  up 
the  difference  in  flange  stress 
between  those  two  sections. 

The  discussion   just  given 
will  be  the  means  of  giving  us  the 

number  of  rivets  required  between  any  two  sections;  but  it  does  not 
give  us  the  rivet  spacing  between  these  two  sections.  In  order  to 
determine  the  rivet  spacing  at  any  particular  point,  the  following 
analysis  is  presented  (see  Fig.  144). 

Let  If,  =  Moment  at  one  section, 

M2  =  Moment  at  another  section  nearer  center  of  girder  than  the  section 

where  Af,  occurs; 

V    =  Shear  at  section  where  Af ,  occurs; 
v    =  Amount  of  flange  stress  one  rivet  can  transfer;  or  it  is  the  stress  on 

one  rivet ; 

s    =  Distance  between  the  two  sections; 
n    =  Number  of  rivets  between  the  two  sections. 


Fig.  144.    Determination  of  Rivet  Spacing. 


Then, 


--1  =  Flange  stress  due  to  moment  M , ; 

lie 

—2  =  Flange  stress  due  to  moment  M2; 
he 

2 i  _  Difference  of  flange  stress  between  the  two  sections; 

he         «• 

/  Afj  _  A_,  \    ^  v  =  n^  jfumber  Of  rivets  required  in  space  s. .  .(1 ) 

\  he  he    J 


173 


164 


BRIDGE  ENGINEERING 


If  the  above  sections  be  taken  close  enough  together  so  that 
the  number  of  rivets  required  will  be  1  (that  is,  n  =  1),  then  V 
can  be  considered  as  constant  between  the  two  sections,  and  then 
the  moment  M2  =  Mt  +  Vs  (see  Article  44,  Part  I).  Substituting 
in  Equation  1,  above,  there  results: 


from  which, 

*->, 

which  is  the  formula  for  the  rivet  spacing  in  the  vertical  parts  of  the 
flanges  of  any  girder,  providing  the  flange  is  not  subjected  to  localized 
loading.  It  is  to  be  used  for  the  rivet 
spacing  in  both  the  top  and  bottom 
flanges  of  through  girders,  but  not  in 
the  top  flanges  of  deck  plate-girders  for 
railroad  service.  It  is  to  be  used,  how- 
ever, in  the  bottom  flanges  of  deck  plate- 
girders  for  railroad  service.  The  dis- 
tance /ie  is  not  ordinarily  used,  the 
distance  between  rivet  lines  being  used 
instead  (see  Fig.  145).  The  rivet  spacing 
in  the  cover-plates  and  horizontal  legs  of 
the  angles  is  made  to  stagger  with  that 

in  the  vertical  legs,  and  usually  the  staggering  is  with  every  other  rivet 
in  the  vertical  flange.  The  term  stagger  signifies  that  the  rivets  in 
the  top  flange  are  not  placed  opposite  the  rivets  in  the  vertical  legs 
of  the  flange  angles  —  or,  that  in  case  there  are  two  lines  of  rivets 
in  the  vertical  legs  of  the  angle,  a  rivet  near  the  outer  edge  of  the 
cover-plate  is  placed  in  the  same  section  wrhere  a  rivet  occurs  near  the 
lower  edge  of  the  vertical  legs  of  the  angle,  and  vice  versa. 

EXAMPLES  FOR  PRACTICE 

1.  Determine  the  rivet  spacing  at  a  section  where  the  shear  is  147  200 
pounds,  the  value  of  one  rivet.  4  920  pounds,  and  the  effective  depth  of  the 
section  84£  inches. 

ANS.     2.82  inches. 

2.  Determine  the  stress  on  a  rivet  at  a   section  where  the  shear  is 
299  400  pounds,  the  spacing  2\  inches,  and  the  effective  depth  of  the  girder 
84}  inches. 

ANS.     8  870  pounds. 


Fig.  145.    Determination  of  Rivet 
Spacing.     - 


174 


BRIDGE  ENGINEERING 


165 


The  rivet  spacing  is  usually  determined  at  the  tenth-points; 
and  a  curve  is  plotted  with  the  spacing  as  ordinates  and  the  tenth- 
points  as  abscissae.  The  rivet  spacing  at  any  intermediate  point  can 
be  determined  from  this  curve.  When  one-eighth  the  gross  section 
of  the  web  is  considered  as  flange  area,  then  only  that  proportion  of 
the  shear  which  is  transferred  to  flanges  is  to  be  considered  in  com- 
puting the  rivet  spacing,  on  account  of  the  fact  that  some  of  the 
shear  is  transferred  directly  to  the  bending  moment  in  the  web. 

In  order  to  determine  the  distance  between  rivet  lines,  the 
gauge,  or  distance  out  from  the  back  of  the  angles  to  the  place  where 
the  rivets  must  be  placed,  must  be  known  for  different  lengths  of  legs. 
Table  XXI  gives  the  standard  gauges,  and  also  the  diameter  of  the 
largest  rivet  or  bolt  which  is  allowed  to  be  used  in  any  sized  leg.  No 
gauges  should  be  punched  otherwise  unless  your  large  experience  or 
instructions  from  one  higher  in  authority  demand  it,  and  this  should 
be  so  seldom  that  indeed  it  might  be  said  never  to  be  necessary. 

TABLE    XXI 

Standard  Gauges  for  Angles 
(All  dimensions  given  in  inches) 


MAXI- 

MAXI- 

MAXI- 

L 

a 

MUM 
RIVET 
ou    BOLT 

L 

g. 

MUM 
RIVET 
OR   BOLT 

L 

(/ 

MUM 
RIVET  OR 
BOLT 

8 

7 

4* 

31 

2 

it 

j 

2 

l! 

H 
l 

' 

6 

3* 

- 

2| 

if 

| 

i| 

1 

5 

3 

1 

2i 

it 

a 

J 

4 

21 

21 

H 

f 

i 

L 

Oi 

02 

L 

„ 

02 

8 

3 

3 

6* 

2i 

2 

7 

2J. 

0 

5 

2 

1 

G 

21 

2$ 

"When  thickness  is  J  inch  or  over. 


175 


166 


BRIDGE  ENGINEERING 


Fig.  146.    Determination  of 
Distance  between 


The  distance  between  rivet  lines  for  the  girder  being  designed 
(see  Fig.  146),  is,  in  the  first  case: 

h,  -  h  -   (29l  +   ^) 

=  74.25  -  (2  X  1\  +  2J) 
=  67 . 00  inches. 

In  the  second  case,  where  |  of  the  web  is 
considered,  the  above  distance  is  74.25  — 
(2  X  2J  +  24)  =  67.25  inches.  The  compu- 
tations and  the  rivet  spaces  at  the  tenth- 
point,  and  at  the  ends  of  the  cover-plates  in 
the  bottom  chord  of  the  plate-girder,  are 
shown  for  each  case  in  Table  XXII.  The 
value  of  v  is  the  value  of  a  |-inch  rivet  in 
bearing  in  a  f-inch  web  (see  Specifications, 
Article  40,  and  Carnegie  Handbook,  p.  195, 
second  table).  This  value  is  4  020  pounds. 

In  the  first  column,  7.98—  indicates  that 
the  end  of  the  cover-plate  next  to  the  flange 

is  7.98  feet  from  the  end  of  the  girder,  and  that  this  section  is  taken 
just  to  one  side  of  that  point,  the  side  being  that  nearest  the  end  of 
the  girder.  In  a  similar  manner,  7.98+  indicates  that  the  section 
'is  taken  to  that  side  of  the  point  which  is  nearest  the  center  of  the 
girder.  A  like  interpretation  should  be  placed  on  15.55—  and 
15.55  +  ,  the  point  under  consideration  in  this -case  being  the  end  of 
the  outer  or  top  cover-plate. 

In  the  fifth  column,  values  are  given  which  indicate  that  portion 
of  the  shear  which  is  transferred  to  the  flanges.  For  example, 

Oq?  ™    »n  =  74  700,  and  the  difference  between  97  700  and 

74  700  represents  that  portion  of  the  shear  which  is  taken  up 
directly  by  the  web  in  the  form  of  bending  moment.  An  inspection 
of  the  headings  of  the  third  and  fourth  columns  will  tend  to  make 
this  matter  clearer. 

Where  there  is  local  loading,  as  in  the  top  flange,  the  rivets,  in 
addition  to  the  stress  caused  by  the  transferring  of  web  stresses,  are 
stressed  by  the  vertical  action  of  the  angles  being  pressed  downward 
by  the  ties  and  the  consequent  upward  pressure  of  the  web.  Accord  - 


176 


BRIDGE  ENGINEERING 


107 


TABLE     XXII 
Rivet  Spacing  in  Bottom   Flange 

Flange  Taking  All  the  Moment 


SECTIOX 

TOTAL  SHEAR 
(Pounds) 

ft, 

(Inches) 

(Pounds) 

RIVET 
SPACING 
(Inches) 

REMARKS 

0 

117800 

67 

4290 

2.80 

1 

97  700                    67 

4290 

3.38 

2 

79  300                   67 

4290 

4.16 

3 

61  300                   67 

4290 

5.38 

4 
5 

44200 
28  600 

67 
67 

4290 
4290 

7.46 
11.52 

I  See  Specifica- 
\  tions,  Art.  54 

One-Eighth  of  Web  Area  Considered 
hr  «=  67.25  inches;  v  -  4  920  pounds 


SECTION 

TOTAL  SHEAR 
(Pounds) 

NET  FLANGE 
AREA  PLUS  i 
WEB  AREA 
(Sq.  Inches) 

NET  FLANGE 
AREA 
(Sq.  Inches) 

REDUCED 
SHEAR 
(Pounds) 

RIVET 
SPACING 
(Inches) 

0 

117800 

14.08 

10.61              88800 

3.75 

1                        97  700 

14.08 

10.61              74700 

4.45 

7.98- 

90000 

14.08 

10.61 

67  900 

4.88 

7.98  + 

90000 

20.08 

16.61 

74800 

4.42 

2 

79  300 

20.08 

16.61 

65800 

5.02 

15.55- 

67500 

20.08 

16.61 

56  000 

5.81 

15.55  + 

67500 

24.58 

21.11 

58  100 

5.69 

3 

61  300 

24.58 

21.11     . 

52  700 

6.28 

4 

44200 

24.58 

21.11 

38000 

8.71 

5 

28600 

24.58 

21.11 

24  600 

13.42 

ing  to  Article  15  of  the  Specifications,  the  weight  of  one  driver  is 
distributed  over  three  ties  (see  Fig.  147). 

W 

Let  — j-  ,  =  iv,  the  load  per  linear  inch  caused  by  one  wheel  W,  which 

load  is  assumed  to  be  uniformly  distributed  over  the  dis- 
tance /; 

ws  =  i'i ,  the  vertical  load  or  stress  that  comes  on  one  rivet  in  the 
space  s; 

v  =  -T—  ,  the  stress  on  a  rivet   due  to  the  distribution  of  flange 
stresses  when  s  is  a  space,  and  V  the  shear  at  that  point. 

When  these  two  stresses  act  on  the  rivet,  the  maximum  stress  will 
be  vn,  the  ultimate  amount  that  it  is  allowed  to  carry,  and  this  will 
act  as  shown  in  Fig.  147 :  Then, 


177 


168 


BRIDGE  ENGINEERING 


+  (ws)2 


from  which, 


which  gives  the  spacing  at  any  point  in  the  girder  flange  under 
localized  loading.  Note  that  if  w  equals  zero — that  is,  if  there  is  no 
localized  loading — there  results: 


which  is  the  same  as  previously  deduced  for  flanges  with- 
out localized  load- 
ings. 

The  rivet  spacing 
for  the  top  flange 
of  the  girder  Which 
is  being  designed 
is  given  in  Table 
XXIII.  Here  W 
=  20000;  /  =  (3X 
7  +  3  X  6)  =  39 

.     ,  20  000 

inches;  w  =  — -~ 

=  513;  hr  =  67 
inches;  and  vw  = 
4  920  pounds,  which 
is  the  bearing  of  a 
| -inch  rivet  in  the 
f-inch  web.  The 
top  cover-plate  is 
run  theentire  length 
of  the  span. 


Fig    147.    Rivet  Spacing  Determined  by  Stresses  Distributed 
under  Localized  Loading. 


178 


BRIDGE  ENGINEERING 


109 


TABLE    XXIII 
Rivet  Spacing  in  Top  Flange 

Flange  Taking  All  the  Moment 


SECTION 

w- 

TOTAL  SHEAR 
(Pounds) 

or 

V(x)°- 

RIVKT  SPACE 
(Inches) 

0 
1 
2 
3 
4 
5 

262600 

- 

117800 
97700 
79  300 
61  300 
44200 
28600 

3  080  000 
2  140000 
1  390  000 
840000 
435000 
181500 

1  825 
1  550 
1  285 
1  050 
835 
660 

2.70 
3.17 
3  .  83 
4.68 
5.88 
7.45 

One-Eighth  of  Web  Area  Considered 
w  =  513;  ht  =  67i  inches;  ru  =  4  920  pounds. 


SKCTIO.N    .   u?2 

REDUCED 
SHEAR 
(Pounds) 

(*)• 

RIVET  SPACE 
(Inches) 

var- 

0 

262600 

97600 

2  100  000 

1  538 

3.20 

1      262  600 

81  000    1  450  000 

1315 

3.74 

2 

262  600 

65  800  !  985  000 

1  100 

4.50 

15.55- 

262600 

56000 

695  000 

980 

5.02 

15.55  + 

262  600 

58  100 

765  000 

1  014 

4.85 

3 

262  600 

52  700 

616  000 

938 

5.24 

4 

262600 

38000 

320  000       763 

6.44 

o 

262  600 

24600 

134  000       629 

7.82 

The  points  other  than  the  tenth-points  referred  to  in  the  first  column 
are  for  sections  taken  just  to  the  left  and  right  of  the  top  cover-plate. 
The  values  of  the  reduced  shears  given  in  the  third  column  are  ob- 
tained as  has  been  previously  explained.  Although  the  rivet  spacing 
in  the  lower  flange  is  considerably  greater  than  that  in  the  upper 
flange,  and  accordingly  a  smaller  number  of  rivets  would  be  required, 
yet  the  spacing  in  the  lower  flange  is  made  the  same  as  that  in  the 
upper.  Convenience  in  the  preparing  of  plans  and  facility  in  manu- 
facture make  this  action  economical.  Theoretical  spacing  greater 
than  6  inches  should  be  dealt  with  according  to  Article  54  of  the 
Specifications. 

The  values  of  the  rivet  spacing  given  in  Tables  XXII  and  XXIII 
are  plotted  in  Fig.  148.  Note  that  the  effect  of  the  localized  loading 
is  to  decrease  the  rivet  spacing,  and  also  note  that  the  effect  increases 
from  the  ends  toward  the  center. 


179 


170 


BRIDGE  ENGINEERING 


Note.-5ccond  Cover  Plate  oi 

Top  Flanoc  Lxtends  Lntire 
Length,  of  Oirdcr. 


Fig.  148.    Plotted  Values  of  Rivet  Spacing  Given  in  Tables  XXII  and  XXIII. 


180 


BRIDGE  ENGINEERING 


171 


The  size  of  the  flange  angles  and  the  width  of  the  cover-plates 
for  different  spans,  are  a  matter  of  choice.  Once  the  size  is  deter- 
mined, the  thickness  can  be  computed.  The  sizes  very  generally 
adopted  in  practice  are  as  follows: 


SPANS 


WIDTH  OF  COVER-PLATE 


15  to    20  feet 

5  x  3J  inches 

none 

20' 

25 

6x4 

'  ' 

25' 

40 

6x6 

" 

40' 

75 

6x6 

14 

inches 

75' 

100 

6x6 

16 

" 

100  '     120 

8x8 

20 

" 

For  another  method  of  the  presentation  of  this  subject,  see 
"Steel  Construction,"  Part  IV,  pp.  264  to  268. 

EXAMPLE    FOR    PRACTICE 

1.  Determine  the  rivet  spacing  for  the  top  chord  of  a  plate-girder, 
loading  E  40,  and  7  by  9-inch  ties  being  used.  The  web  is  £  inch  thick; 
distance  from  back  to  back  of  angles,  6  feet  6|  inches;  flange  angles,  6  by  6 
by  ^-inch;  and  cover-plate,  14  by  ^-inch,  two  f-inch  rivets'being  out  of  each. 
First,  consider  the  flange  as  taking  all  the  bending  moment;  and  second, 
consider  one-eighth  the  gross  area  of  the  web.  The  total  unreduced  shear 
is  80  000  pounds  in  both  cases. 

ANS.     3.21  inches;  3.  76  inches. 

74.  Lateral  Systems  and  Cross=Frames.  There  are  two  methods 
in  use  in  common  practice  in  determining  where  the  panels  of  the 
lateral  bracing  shall  fall — namely,  (1)  To  choose  the  number  of  panels 
so  that  the  panel  points  come  opposite  the  stiffness,  and  (2)  to  choose 
the  number  of  panels  so  that  the  placing  of  the  panel  points  is  inde- 
pendent of  the  stiffener  spacing.  The  lateral  systems  should  be  of 
the  Warren  type;  and  in  both  of  the  above  cases  the  angles  that  the 
diagonals  make  with  the  girder  should  not  be  greater  than  45  degrees. 
Also,  it  is  best  to  have  all  panels  the  same  length  and  to  have  an  equal 
number  of  panels.  This  latter  condition  will  simplify  the  drafting 
very  much,  since  one-half  of  one  girder  can  be  drawn  and  the  other 
half  will  be  symmetrical,  the  opposite  girder  being  similar  to  the  one 
drawn,  but  being  left-handed. 

The  members  of  the  lateral  systems  will  take  tension  or  com- 
pression according  to  the  direction  the  wind  blows.  Cross-frames 
are  placed  at  intermediate  points  to  stiffen  the  girders.  These  are 


181 


ftfii?* 

1"^§  s 
*!•*  1  ? 

"S  si'vj1^    l"§  ^>"^  leS'Sai    ^  S  ^>^ 

1IJU  II^IP^  fill 


BRIDGE  ENGINEERING  173 

diagonal  bracings  (see  Plate  II),  and  are  placed  at  certain  intervals 
according  to  the  judgment  of  the  engineer.  Good  practice  demands 
that  their  number  should  be  about  as  indicated  below : 

SPAN  OF  GIRDEII  NUMBER  OF  CROSS-FRAMES 


0  to     20  feet 
20  to      35     " 
3.5  to     70     " 
70  to     85     " 

85  to  110     " 


The  above  is  not  intended  to  serve  as  a  hard  and  fixed  rule.  Varia- 
tions from  the  limits  given  are  to  be  made  as  the  case  demands.  In 
all  cases  they  are  put  at  the  panel  points  of  the  bracing,  the  top  and 
bottom  parts  acting  as  sub-verticals  in  the  lateral  system.  Also,  the 
cross-frames  should  divide  the  span  into  equal  parts  if  possible.  In 
cases  where  that  is  not  possible,  the  shortest  divisions  should  come 
near  the  ends  of  the  spans. 

If  the  panel  points  are  to  be  located  at  the  stiffeners,  the  number 
of  panels  is  a  function  of  the  depth  of  the  girder  (see  Specifications, 
Articles  47  and  48) .  In  this  case  the  number  of  panels  is  given  by : 

,.  _  Span  in  inches. 

Depth  of  girder  in  inches' 

no  fraction  being  considered.  As  an  example,  let  it  be  required  to 
determine  the  number  of  panels  in  a  girder  85  feet  center  to  center 
of  bearings,  the  depth  being  90|  inches  back  to  back  of  angles.  Then, 

85  X  12 
N  =  -^  ------  =  1 1 . 3,  or,  say,  1 1  panels. 

yu .  — o 

Each  panel  will  then  be  92.8  inches  long.  This,  according  to  Article 
47  of  the  Specifications,  being  greater  than  5  feet,  would  not  be  allowed 
as  a  space  between  two  stiffeners;  but  one  stiffener  can  be  placed  in 
between,  and  then  the  panel  points  will  come  at  every  other  stiffener. 
The  cross-frames  should  be  five  in  number. 

The  arrangement  of  panels  and  cross-frames  is  shown  in  Fig. 
149.  Here  the  cross-frames  are  marked  C.  F.,  and  the  broken  lines 
represent  the  lower  lateral  system. 

In  case  an  even  number  of  panels  were  desired,  then  ten  would 
be  the  number  chosen  and  the  general  arrangement  would  be  as 
shown  in  Fig.  150.  The  length  of  a  panel  would  be  85  X  12  -s- 


183 


174 


BRIDGE  ENGINEERING 


10  =  102  inches,  or  8  feet  6  inches,  which  would  allow  of  one  stiffener 
in  between  and  still  keep  the  stiffener  spacing  within  the  limit  of 
5  feet. 

The  cross-frames  at  the  ends  of  the  span  are  designated  as  end 
cross-frames,  and  those  in  between  are  designated  as  intermediate 
cross-frames. 

In  case  the  spacing  of  the  stiffeners  is  not  required  to  be  such  as 
to  coincide  with  the  panel  points  of  the  lateral  bracing,  the  panel 
length  will  depend  upon  the  spacing  of  the  girders,  being  equal  to  or 


Fig.  150. 
Arrangements  of  Panels  and  Cross-  Frames. 

greater  than  the  spacing  in  order  to  keep  the  angle  which  the  diagonals 
make  with  the  girder  less  than  45  degrees.     In  this  case, 

,T  Span  in  feet 

Distance  center  to  center  of  girders  in  feet 

For  the  girder  considered  on  page  1  74,  the  number  of  panels  would  be 

OK 

-——  =  11.3  —  or,  say,  11  panels  —  if  odd  numbers  were  to  be  used, 
7.5 

and  12  if  even  numbers  were  to  be  desired. 

For  the  case  in  hand,  the  panel  points  of  the  bracing  will  be  taken 
at  the  stiffeners,  and  an  even  number  of  panels  will  be  used.     Then, 

W_  511?..  9. 


The  arrangement  of  the  panels  and  cross-frames,  and  also  the  maxi- 
mum stresses  in  the  diagonals,  are  shown  in  Plate  II,  the  stresses  being 
determined  according  to  Article  50,  Part  I,  "Bridge  Analysis,"  and 
Article  24  of  the  Specifications.  All  the  wind  is  taken  as  acting  on 
one  side  of  the  bridge;  and  no  overturning  effect,  either  on  the  girder 


184 


BRIDGE  ENGINEERING 


.  175 


or  on  the  train,  is  considered.  Also,  note  that  the  wind  stresses  in  the 
flanges  are  not  considered.  Should  the  student  determine  these,  he 
will  find  them  too  small  to  be  considered  according  to  Specifications, 
Article  39. 

Before  designing  the  lateral  diagonals  which  consist  of  one  or 
two  angles,  Articles  31,  33,  34,  35  (last  portion),  38,  40,  63,  and  83  of 
the  Specifications  should  be  care- 
fully studied.     The  upper  lateral 
bracing  is    to  be  designed  first. 
Carnegie  Handbook,  pp.  109  to 
119,  is  to  be  used. 

The  member  U^Ul  must  be 
designed  for  a  compressive  stress 
equal  to  23.20  +  0.8  X  20.6 
=  —39.68,  and  a  tensile  stress  of 
20.6  +  0.8  X  20.6  =  +  37.08.  The 
length  of  the  diagonal  measured 
from  center  to  center  of  girders 
is  1/6.5'-'  +6.22  -  9  feet,  or  108 
inches.  In  reality  the  length  is  not 

108  inches,  as  the  cover-plate  takes  off  a  certain  amount,  as  shown 
in  Fig.  151.  The  true  length,  which  is  to  be  taken  as  a  column  length 
in  designing,  is  108  —  2y,  and  y  is  readily  computed  to  be  9.70  inches, 
thus  making  the  true  length  88.6  inches.  The  least  allowable  rectan- 
gular radius  of  gyration  is  obtained  from  the  relation  that  the  greatest 

value  of  -  =  120,  and  therefore  the  least  value  of  r  =  — —  =  0.74. 
r  120 

It  will  be  assumed  that  a  6  by  4  by  r96-inch  angle  with  an  area  of  • 
5.31  square  inches  will  be  sufficient.  Here  the  length  equals  88 . 60 
inches,  and  the  least  rectangular  radius  of  gyration  is  1 . 14;  hence, 

88.60 


Fig.  151.    Determination  of  Length  of 
Diagonal  in  Lateral  Bracing. 


The  required  area  is 


=  13  000  -  60  X 

=     8  330  pounds  per  square  inch. 

39  360 


8330 


4 . 73  square  inches.     As  the   angle 


assumed  has  an  area  of  5.31  square  inches,  which  is  considerably 
greater  than  the  4.73  square  inches  required,  this  angle  cannot  be 
used,  and  other  assumptions  must  be  made  until  the  area  of  the  angle 


185 


170 


BRIDGE  ENGINEER  ING 


assumed  and  the  required  area  as  computed  are  equal  or  very  nearly  so. 

A  6  by  4  by  ^-inch  angle  with  an  area  of  4.75  square  inches  will 

now  be  assumed.     The  length  is  88 . 60  inches  as  before,  and  the  least 

rectangular  radius  of  gyration  is  1.15.     The  unit-toad  P  =  8340 

pounds  per  square  inch,  and  the  required  area  is-^     —  =  4 . 72  square 

8  340 

inches.     As  the  area  of  the  angle  assumed  and  the  required  area  as 
computed  are  very  close,  this  sized  angle  will  be  used. 

The  section  must  now  be  examined  for  tension,  and  in  order  that 
both  legs  of  the  angle  may  be  considered  as  effective  section,  both  legs 

must  be  connected  at  the  end.   The  area  required  will  be  '— - 


2.04  square  inches. 


Considering  one  rivet-hole  is  taken  out  of  the 
angle,  the  net  area  is  4 . 75  —  1  X 
(I  +  i  )  X  i  =  4 . 25  square  inches, 
which  is  amply  sufficient. 

If  the  4-inch  leg  only  were  as- 
sumed to  be  connected,  the  grcss 
area  would  be  4  X  %  =  2. CO 
square  inches,  and  the  net  area 
would  then  be  2.00  -  1  X  (I  + 
I )  X  -^-inch  =  1 .50  square  inches, 
which  is  not  sufficient.  If  the 
6-inch  leg  were  connected,  the 
area  would  be  sufficient.  See  Fig. 
152  for  method  of  connection  and 
rivets. 

The  number  of  rivets  required  (see  Specifications,  Article  38 
and  40)  is  computed  as  follows:  If  the  member  were  not  subjected 
to  both  tension  and  compression,  the  number  of  rivets  required  in 
single  shear  would  be: 

= 39360          

(9000  +  50  per  cent  of  9  000)  X  0.6013 
=  39360 
8100 

=  4. 86  (say  5). 

But  according  to  Article  38  of  the  Specifications,  this  number  must  be 
increased  50  per  cent,  and  accordingly  4.86  X  li  —.7. 29  (say  8) 


Fig.  152.  Method  of  Connecting  Angle  Legs 
in  Lateral  Bracing  and  Cross-Frames. 


186 


w  ^ 

°  "i 

M    -° 

15 


BRIDGE  ENGINEERING  177 

shop  rivets  are  to  be  used.  In  the  above  formula,  0.6013  is  the  area 
of  the  cross-section  in  square  inches  of  a  |-inch  rivet.  In  order  that 
both  legs  should  be  connected,  a  clip  angle  as  shown  in  Fig.  152  is 
used ;  and  the  same  number  of  rivets  must  go  through  both  legs  of  the 
clip  angle,  since  the  stress  in  the  vertical  leg  of  the  main  angle  is 
transferred  to  the  clip  angle  and  from  there  into  the  connecting  plate. 

The  above  number  of  rivets  makes  the  joint  safe  so  that  it  will 
not  shear  off  in  the  plane  between  the  connection  plate  and  the  hori- 
zontal leg  of  the  angle.  The  joint  must  also  be  designed  so  that 
there  will  be  sufficient  rivets  in  bearing  to  prevent  them  from  tearing 
out  of  the  connecting  plate.  The  number  required  is: 

_  39  360     

"  (15  000  +  50  per  cent  of  15  000)  X  $  X  $ 
_  39  300 
7~380 
=  5.34. 

This  5.34  must  be  increased  50  per  cent,  making  a  total  of  5.34 
X  1.5  =  8.01  =  say,  8  shop  rivets  as  before. 

The  above  rivets  are  shop  rivets,  since  it  is  assumed  that  the  span, 
being  a  small  one,  will  be  riveted  complete  in  the  shop  and  shipped  to 
the  bridge  site  ready  to  place  in  position  without  any  further  riveting. 
In  case  the  girders  are  shipped  separately,  then  the  lateral  bracing 
must  be  riveted  up  in  the  field ;  and  according  to  last  part  of  Article 
40  of  the  Specifications,  the  rivets,  being  field  rivets,  must  have  the 
allowed  unit-stresses  reduced  one-third,  which  is  equivalent  to  having 
the  number  of  shop  rivets  increased  50  per  cent.  This  will  make  the 
required  number  of  field  rivets  8  X  1.5  =  12. 

As  a  rule,  the  connection  plates  are  |-  inch  thick,  seldom  more. 
Also,  the  members  of  the  upper  lateral  system  are  connected  on  the 
lower  side  of  the  connection  plate  in  order  not  to  interfere  with  the 
ties.  Note  that  the  use  of  the  clip  angles  requires  a  smaller  connec- 
tion plate  than  would  be  necessary  if  these  angles  were  not  used,  since 
in  the  latter  case  all  the  rivets  must  then  be  placed  in  one  row  in  the 
horizontal  leg  of  the  angle. 

The  number  of  rivets  required  in  the  connection  plate  and  the 
flange  of  the  girder  must  be  sufficient  to  take  up  the  component  of 
that  member  parallel  to  the  girder.  For  the  case  in  hand,  the  num- 
ber (see  Fig.  153)  is:  » 


187 


178 


BRIDGE  ENGINEERING 


x    _6\2 

~s  ~  <To' 
from  which, 

x  =  5.5  (say  6)  rivets. 

Additional  rivets  should  also  be  put  in,  in  order  to  take  up  the  compo- 
nent of  the  other  lateral  diagonal  which  meets  at  this  point. 

The  member  L7/  U1  is  to  be  designed  for  a  maximum  compressive 
stress  of  •  20 . 6  +  0 . 8  X  16 . 0  =  -  33 . 4.     A  6  by  4  by  j76-inch  angle 

with  an  area  of  4.18  square 
inches  will  be  assumed.  The 
least  rectangular  radius  of  gyra- 
tion is  1.16.  The  unit  allowable 
load  is: 

00       f> 

p  =  is  ooo  -  oo  x  f       =  8  42° 

1 .  lo 


Uo 


6.-SH 


Fig.  153.    Calculation  of  Rivets  in  Connection 
Plate  and  Flange  of  Girder. 


pounds  per  square  inch. 

™,             .                .    33400 
Ihe  required  area  is  -— = 

3 . 97  square  inches.  As  this  is 
very  near  the  area  assumed,  and 
as  trials  with  other  angles  do 
not  give  required  areas  which 
come  any  closer,  this  angle  will 
be  used. 

The  rivets  required  in  single 
shear  are: 


33  400 


X  1.5  =  6.21  (say  7)  shop  rivets,  and 


8  100 
G. 21  X  1.5  =  9.3  (say  10)  field  rivets. 

The  rivets  required  in  bearing  in  the  f -inch  connection  plate  are : 

oo  4-nn 

-'----„  X  1 .5  =  6.78  (say  7)  shop  rivets,  and 
7  ooU 

*  6.78  X  1.5  =  10.17  (say  11)  field  rivets. 

The  above  computations  show  the  joint  to  be  weakest  in  bearing, 
and  therefore  7  shop  or  11  field  rivets  must  be  used.  It  is  not  neces- 
sary to  investigate  this  member  for  tension,  as  the  computations  for 
the  first  diagonal  indicate  that  the  area  will  be  sufficient,  both  legs 
being  connected. 

The  member  UJJ2f  must  be  designed  for  a  maximum  compres- 
sive stress  of  16.0  -f-  0.8  X  14.1  =  -27.28.    A  6  by  4  by  f-inch 


188 


BRIDGE  ENGINEERING  179 


angle  with  an  area  of  3.61  square  inches  and  a  least  rectangular 
radius  of  gyration  of  1.17  will  be  assumed.  The  unit-stress  P,  as 
computed  from  the  formula  in  the  Specifications,  is  8  460  pounds  per 

27  9SO 
square  inch;  and  the  required  area  is        "       =  3  .  23  square  inches. 


This  angle  will  be  used,  as  the  given  and  required  areas  are  close 
together,  and  as  the  next  smaller  angle  —  a  6  by  3  i  by  f-inch  angle 
with  an  area  of  3.42  square  inches  —  gives  a  required  area  of  3.58 
square  inches,  thus  being  too  small. 

The  rivets  required  in  single  shear  are  : 

27  280 

—  X  1  •  5  =  5  .  04  (say  5)  shop  rivets,  and 

8  1UU 

5.04  X  1.5  =  7.6  (say  8)  field  rivets. 
The  rivets  required  in  bearing  in  a  f  -inch  web  are  : 

'' 

X  1  .5  =  5  .  54  (say  6)  shop  rivets,  and 


5  .  54  X  1.5  =  8.3  (say  9)  field  rivets. 

In  order  to  make  the  joints  safe,  6  shop  or  9  field  rivets  should  be  used. 
The  member  U2'U2  must  be  designed  for  a  maximum  compressive 
stress  of  9.6  +  0.8  X  8.0  =  -16.00.  A  3i  by  3  by  f-inch  angle 
with  an  area  of  2.30  square  inches  and  a  least  rectangular  radius  of 
gyration  of  0.90  will  be  assumed.  The  unit-stress  P  is  7  090  pounds 

per  square  inch,  and  the  required  area  is  -  -         =  2  .  26  square  inches. 

i  U«JU 

As  the  required  and  the  'actual  areas  are  very  close  together,  this 
angle  will  be  used. 

The  rivets  required  in  single  shear  are  : 

^n  *•  *  •*>  =  2.96  (say  3)  shop  rivets,  and 
o  1UU 

2.96  X  H  =  4.44  (say  5)  field  rivets. 

By  computation  similar  to  the  above,  it  is  found  that  4  shop  or  5 
field  rivets  are  required  in  bearing.  Since  the  bearing  requires  the 
most  rivets  to  make  the  joint  safe,  4  shop  or  5  field  rivets  must  be  used. 

If  the  Specifications  would  have  allowed  a  3^  by  3i  by  j56-inch 
angle  with  an  area  of  2.09  square  inches,  this  angle  would  have 
exactly  fulfilled  the  requirements,  the  required  area  being  2.09 
square  inches. 

The  member  U2U3'  must  be  designed  for  a  maximum  compres- 


189 


180  BRIDGE  ENGINEERING 

sive  stress  of  8.0  +  0.8  X  4.1  =  -11.28.  A3  by  3  by  f-inch 
angle  with  an  area  of  2.11  square  inches  and  a  least  radius  of 
gyration  of  0.91  will  be  assumed.  In  this  case  the  unit-stress  is 
7  160,  and  the  area  required  is  1.58  square  inches.  The  required 
area  is  considerably  less  than  the  area  of  the  angle  assumed;  but  it 
must  be  used,  since  it  is  the  smallest  allowed  by  the  Specifications, 
which  require  that  the  material  shall  not  be  less  than  f-inch,  and 
from  Table  XXI  it  is  seen  that  3  inches  is  the  smallest  size  leg  in  which 
a  |-ineh  rivet  can  be  used. 

The  stresses  in  all  the  members  of  the  lower  lateral  system  are 
less  than  the  stresses  in  the  member  just  designed,  and  therefore  all 
members  of  the  lower  lateral  system  will  be  "made  of  one  3  by  3  by 
f-inch  angle. 

For  the  last  member  designed  in  the  upper  lateral  system,  and 
for  all  members  in  the  lower  lateral  system,  3  shop  or  5  field  rivets 
will  be  required  at  the  ends.  These  are  more  than  sufficient  to  take 
up  the  stress,  but  it  has  been  found  that  less-  than  three  rivets  do  not 
make  a  good  joint. 

The  stress  sheet,  Plate  II,  shows  the  general  arrangement  of  the 
lateral  system,  the  number  of  rivets  in  the  connections  and  also  in  the 
connection  plates  where  they  join  the  flanges. 

The  intermediate  cross-frames  do  not  lend  themselves  to  a  theo- 
retical design,  since  the  stresses  which  come  upon  them  are  not  easily 
ascertained.  It  is  good  practice  to  require  that  all  members  be  of 
the  sizes  as  given  below: 


RIVETS 

SPAN  OF  GIRDKR 

ANGLES 

(in  Feet) 

(in  Inches) 

SHOP 

FIELD 

30  to    65 

34.  -x  34.  x  f 

3 

4 

65  to  110                                 4  x  4  x  f 

4 

5 

The  angles  in  the  intermediate  cross-frames  will  therefore  be  3^  by 
3-1-  by  |-inch. 

The  end  cross-frames  (see  Fig.  154)  act  in  a  manner  somewhat 
similar  to  the  portal  bracing  in  a  bridge,  since  they  transfer  all  the 
wind  which  comes  on  the  top  chord  and  on  the  train  to  the  abutment. 
This  load,  which  acts  at  the  level  of  the  ties,  is  in  this  case  (see  Article 
24  of  the  Specifications): 


190 


BRIDGE  ENGINEERING 


181 


X  61  ft.  9  in. 


=  18  525  pounds. 


It  is  usually  assumed  that  half  of  this  is'  transferred  to  the  point  a  by 
means  of  a-b,  and  from  there  down  a-b'  to  the  masonry.  The  other 
half  goes  directly  down  b-a'  to  the  masonry.  This  causes  stresses  as 
shown  in  Fig.  154.  Note  that  the  stress  in  a-b  will  always  be  com- 
pression; but  the  stresses  in  the  diagonal  will  be  either  tension  or 
compression  according  to  the  direction  the  wind  blows.  The  mem- 
ber a-b  will  be  a 
3-^by  3Hwf-inch 
angle.  To  form 
the  connections  at 
its  end,  3  shop  or 
5  field  rivets  will 
be  used. 

The  maxi- 
mum compressive 
stress  for  which 
the  diagonals  are 
to  be  designed  is 
12.70  +  0.8X12.70 
-22.86.  Here 
the  length  is  108 

inches  if  the  angle  tends  to  bend  one  way;  but  if  it  bends  as 
shown  by  the  broken  lines  in  Fig.  154,  the  length  will  be  one-half 
of  this.  For  this  reason,  angles  with  unequal  legs  should  be  used, 
the  longer  leg  extending  outward.  This  allows  the  greatest  rectan- 
gular radius  of  gyration  to  be  used. 

A  4  by  3  by  j76-inch  angle  with  an  area  of  2.87  square  inches 
and  a  radius  of  gyration  of  1 .25  will  be  assumed.  The  unit-load  P 
is  computed  to  be  8  750  pounds,  and  the  required  area  is  therefore 
22  860  -=-  8  750  =  2.61  square  inches.  This  does  not  coincide  very 
closely  with  the  given  area,  but  will  be  used  since  this  angle  comes 
nearer  to  fulfilling  the  condition  than  any  of  the  other  sizes  rolled. 
The  joint  will  require  more  rivets  in  bearing  than  in  single  shear. 
It  is  not  necessary  to  perform  the  complete  computations  in  order  to 
determine  this,  since  a  comparison  of  the  values  of  a  rivet  in  single 
shear  and  in  bearing  shows  that  the  value  in  bearing  is  less  than  that 


Fig.  154.    Action  of  End  Cross-Frames. 


101 


182 


BRIDGE  ENGINEERING 


in  single  shear,  and  therefore  the  number  of  rivets  required  in  bearing 
will  be  greater  than  that  number  required  in  single  shear.  The 
number  of  rivets  required  in  bearing  is: 


^K— — j— p  ~  sav>  ^  shop  rivets,  and 

4.00  X  1.5  =  6  field  rivets. 

75.  The  Stiffeners.  According  to  Article  47  of  the  Specifica- 
tions, these  should  be  placed  at  certain  intervals  whenever  the  unit- 
shear  is  greater  than 

S  =  10  000  -  75  X  (~  =  10  000  -  14  800  =   -4  800  pounds. 


This  negative 
sign  signifies  that 
whenever  the 
unit  shearing 
stress  is  greater 
than  zero,  the 
stiffeners  must  be 
placed  through- 
out the  entire 
length  of  the 
span  at  distances 
not  to  exceed  5 
feet. 

The  interme- 
diate stiffeners 
should  have  the 
outstanding  leg 
long  enough  to 
give  good  sup- 
port to  the  flange  angle  (see  Fig.  155).  The  filler  bars  or  fillers 
are  put  in  so  as  to  allow  the  stiffener  angles  to  remain  straight 
throughout  their  entire  length;  otherwise  they  will  have  to  be 
bent  as  shown  in  Fig.  156.  This  bending  is  called  crimping. 
Stiffeners  must  also  conform  to  Article  48  of  the  Specifications. 
This  would  require  a  different  sized  stiffener  at  each  point,  and  also 
a  different  number  of  rivets  in  each  stiffener.  This  is  not  usually 
done  in  practice.  In  practice  the  stiffener  for  the  first  intermediate 


Section  A-A 


Fig.  155.    Use  of  Straight  Stiffeners,  with  Filler  Bars. 


102 


BRIDGE  ENGINEERING 


183 


point  is  designed,  and  the  remainder  are  made  the  same  in  size  and 
have  the  same  number  of  rivets.  An  exception  to  this  is  where  a 
stiffener  comes  at  a  web  splice.  In  this  case  the  size  is  usually  kept 
the  same,  but  the  number  of  rivets  is  changed  somewhat  to  conform 
to  the  requirements  of  the  splice  design. 

The  second  intermediate  stiffener  comes  at  the  first  tenth-point, 
and  is  6.175  (say  6.2)  feet  from  the  end,  since  it  is  at  the  first  panel 
point,  or  opposite  the  first  panel  point,  of  the  lateral  system.  The 
first  stiffener  will  be  3 . 1  feet  from  the  end ;  and  scaling  off  the  value 
of  the  shear  at  this  point  (see  Fig.  134),  it  is  found  to  be  108000 


Fig.  156.     Crimping  of  Stiffener  Aiiglt 
'  where  No  Filler  Bars  are  Used. 


Fig.  157.    Section  of  Intermediate  Stiffener 
Construction. 


pounds.  Here  the  length  I  to  be  used  in  the  formula  for  the  unit 
allowable  compressive  stress  is  74£  —  2  X  f  =  72.75  inches,  the  f 
being  the  thickness  of  the  flange  angle.  The  section  of  the 
material  which  according  to  Article  48  of  the  Specifications  is  to  be 
considered  as  a  column,  is  shown  in  Fig.  157.  The  assumed 
column  cannot  bend  about  the  axis  B-B,but  about  the  axis  A- A, 
and  therefore  the  radius  of  gyration  about  the  axis  A  -  A  must  be 
computed.  The  moment  of  inertia  of  the  fillers  and  the  web  plates 
about  their  own  axes  is  considered  as  zero. 

A  4  by  4  by  ^-inch  angle  with  an  area  of  3 . 75  square  inches  will 
be  assumed  to  be  sufficient  to  withstand  the  stress.  The  moment 
of  inertia  of  this  and  the  filler  bars  and  the  web  portion  is 

/A-A  =  2(5.55  +  3.75  X  2.122  +  3.00  X  0.5632)  =  46.70. 


184 


BRIDGE  ENGINEERING 


&•— 

\ 
\ 
\ 
\ 


x-V 

\0icater 


/: 

Less  thar 


The  radius  of  gyration,  then,  is,  */    ,?''     =  1.764,  and  the  unit-stress 

\  15. (JO 

computed  with  this  value  and  a  length  of  72 . 75  inches  is  8  140  pounds. 
The  required  area  is  now  determined  to  be  108  000  +  8  140  =  13 . 27 
square  inches.  The  value  15.00  used  in  the  above  computation  for 
the  radius  of  gyration  is  the  value  of  the  area  of  the  angles,  the  filler 
bars,  and  the  web  portion.  A  5  by  3^-inch  angle  with  the  5-inch  leg 
out  would  have  given  better  support  to  the  flange,  but  would  not 

make  so  good  a  job,  as  it  would 
have  extended  about  £  inch  be- 
yond the  curved  part  of  the  hori- 
zontal leg  of  the  flange  angle. 

The  bearing  determines  the 
number  of  rivets  in  this  case. 
The  number  is  108000  4-  4  920 
=  22  shop  rivets  in  the  web. 

The  angle  must  now  be  inves- 
tigated in  order  to  see  if  these  22 
rivets  can  go  in  one  row  without 
being  closer  together  than  2| 
inches,  which  is  three  diameters 
of  the  f-inch  rivet.  The  total 
length  in  which  these  rivets  must 

be  placed  is  72.25  inches,  and  therefore  we  have  72.25  -j-  22  =  3.3 
inches  as  a  spacing.  Since  this  is  greater  than  2|  inches,  22 
rivets  can  be  placed  in  one  row.  If  the  spacing  as  determined 
above  had  been  less  than  2f  inches,  it  would  have  been  neces- 
sary to  use  two  rows  of  rivets  spaced  as  shown  in  Fig.  158;  and  then 
the  distance  center  to  center  would  be  more  than  2|  inches,  although 
the  spacing  in  a  vertical  line  would  be  less  than  that. 

The  four  angles  at  the  ends  of  the  girders  are  called  the  end 
stiffencrs.  These  are  placed  in  pairs  on  opposite  sides  of  the  web 
(see  Plate  II,  Article  74). 

The  total  end  shear  is  117  800  pounds,  and  this  is  assumed  to  be 
carried  by  the  two  pairs  of  end-stiffener  angles,  each  carrying  one- 
half.  This  amount  would  require  lighter  angles  than  the  angles 
used  for  intermediate  stiffeners.  It  is  the  customary  practice  to 
make  them  the  same  size  and  thickness  as  the  intermediate  stiffeners, 


Fig.   158.    Rivets  Placed  in  Two  Rows  to 
Give  Necessary  Number  and  Spacing. 


194 


BRIDGE  ENGINEERING 


185 


additional  strength  being  allowed   in  order  to  withstand    the  effects 
of  the  end  cross-frame  when  in  action. 

The  bearing  determines  the  number  of   rivets  required  in  each 


pair  of  stiffeners.     The  number  required  is  — 


117  800 


sn°P 


rivets. 

Some  engineers  arbitrarily  choose  the  stiffeners  regardless  of 
the  shear,  enough  rivets,  however,  being  put  in  the  end  stiffencrs  to 
take  up  all  the  shear;  and  the  spacing  in  the  intermediate  stiffencrs  is 
made  the  same.  One  noted  engineering  firm  determines  its  stiffencrs 
according  to  the  following: 


FLANOE  ANGLE 


STIFFKXERS 


HORIZONTAL 
LEO 

THICKNESS 

END 

IXTEKMEI 

HATH 

4  in. 

Any 

.3x3    x 

Jin. 

3    x  3    x 

I!  in 

o  in. 

Any 

4x4    x 

\  in. 

Six  3-1,  x 

i  in 

6  in. 

Over  |  in. 

4x4    x 

A  in. 

31  x  3.V  x 

s  in 

6  in. 

Less  than  \  in. 

5  x  3i  x 

A  in. 

5    x  3.1  x 

j|-  in 

8  in. 

Any 

6x6    x 

•|  in. 

6    x  4    x 

s  in 

No  rational  method  has  as  yet  been  determined  for  ascertaining 
the  stresses  in  the  stiffeners  of  plate-girders.  Results  obtained  by 
placing  extensomcters  on  the  stiffeners  of  actual  plate-girders  appear 
to  indicate  that  the  stresses  are  very  small,  in  fact  in  most  cases  not 
being  greater  than  1  500  or  2  000  pounds  per  square  inch. 

PROBLEMS    FOR    PRACTICE 

1.  Design,  according  to  Cooper's  Specifications,  the  end   stiffeners  :1 
the  shear  is  150  000  pounds,  the  distance  back  to  back  of  angles  is  6  feet  G^ 
inches,  the  web  £  inch  thick,  and  the  flange  angle  6  by  6  by  ^-inch.    Use  fillers. 

2.  Design  the  intermediate  stiffeners  for  the  girder  of  Problem    1, 
above,  where  the  shear  is  equal  to  75  000  pounds.   L'se  crimped  stiffener  angles. 
Note  that  in  this  case  the  angles  lie  close  against  the  web,  no  filler  bars  being 
used  in  between. 

76.  The  Web  Splice.  Web  splices  are  required  because  of  the 
fact  that  wide  plates  cannot  be  rolled  sufficiently  long.  Web  splice  s 
should  be  as  few  as  possible,  and  good  practice  demands  that  they  be 
placed  at  the  same  points  as  the  stiffener  angle. 

The  tables  on  page  30  of  the  Carnegie  Handbook  give  the  extreme 
length  of  plates  which  can  be  procured  for  any  given  width.  The 


195 


186 


BRIDGE  ENGINEERING 


length  of  plates  for  widths  which  are  not  given  in  these  tables, should  be 
taken  equal  to  the  length  of  the  next  plate  given  whose  width  is  less 
than  that  of  the  desired  plate.  From  the  first  table  it  is  seen  that  a 
74  by  f -inch  plate  can  be  rolled  up  to  400  inches,  or  33  feet  4  inches, 
in  length.  Therefore,  if  the  girder  under  consideration  is  spliced 

at  the  center,  the  web  plates  will  be  required  to  be ~ —       =  30 

feet  10 i  inches,  which  value  does  not  exceed  the  33  feet  4  inches  as 

given  above. 

According  to  Articles  46  and  71  of  the  Specifications,  a  plate  must 

be  placed  on  each 
side  of  the  web  as 
shown  in  Fig.  159, 
and  enough  rivets 
placed  in  each  side 
to  take  the  total 
shear.  The  total 
thickness  of  both 
plates,  and  also 
their  length,  must 
be  sufficient  to 
stand  the  total 
shear,  but  must 
not  be  less  than 
|  inch. 

The  total  shear 
at    the   center  of 

the  girder  under  consideration  (see  Fig.  134,  p.  150)  is  28  600  pounds. 

28  600 
The  area  required  in  each  of  the  two  splice  plates  is    

*£  /\  y  uuu 

^1.59  square  inches;  and  as  their  length  is  62.25  inches,  the 
thickness  must  be  1.59  -f-  62.25  =  0.0255  inch,  but  they  must  be 
made  |  inch  thick  according  to  the  Specifications.  The  width  should 
be  somewhat  greater  than  twice  the  width  of  the  stift'ener  angle  leg. 
This  would  make  the  width  in  this  case  about  10  inches. 

The  bearing  governs  the  number  of  rivets  required  in  this  case, 
and  they  are  28  600  -r-  4  920  =  5.81,  say  6,  shop  rivets.  More  rivets 
than  this  will  be  required  by  practical  considerations,  as  indicated  by 


A-*— J  Section    A-A 

Fig.  159.    Splice  Plates  Placed  on  Each  Side  of  Web. 


196 


BRIDGE  ENGINEERING 


187 


Article  54  of  the  Specifications  or  in  order  to  make  the  spacing  in  the 
stiffener  angle  the  same  as  that  in  the  other  stiffeners.  This  detail 
is  to  be  left  to  the  draftsman,  the  required  number  only  being  put 
on  the  stress  sheet 

In  case  $  of  the  gross  area  of  the  web  is  considered  as  efficient 
flange  area,  then  provision  must  be  made  in  the  splice  for  the  bending 
moment  which  the  web  takes.  A  very  economical  and  efficient  splice 
is  shown  in  Fig.  1GO.  The  horizontal  plates  take  the  stress  due  to  the 
moment,  and  the  vertical  plates  take  the  stress  due  to  the  shear. 

The  web  equivalent  is  3.47  square  inches  and  the  total 
moment  is  1  615  000  pound-feet,  which  is  composed  of  275  000  pound- 


0           0 

0 

o        o       I 

0             0       '    0 

o        o        o 

o   o    o 

O 

o   o    o  .0 

o  o    o 

o 

o   o    o  o 

t) 

(J 

, 

1 

1 

0 

0 

0 

0 

(•Sh  ear  Plat* 

4 

^  6  Shop: 

0 

0 

ke  Shop 

| 

0 

0 

Lii  Shop,' 

0 

o) 

y-  5.^          \ 

600^ 

b 

roo°o°o^ 

o~o"o~ 

o 

0000 

1      o         o        o 

o        o        o  / 

0           0 

g 

o       o        / 

Fig.  160.    Splice  Consisting  of  Vertical  and  Horizontal  Plat 


feet  due  to  dead  load  and  1  340  000  pound-feet  due  to  live  load. 
Therefore  that  proportion  of  the  3.47  which  is  taken  up  by  the  dead 
load  is: 


and  that  proportion  taken  up  by  the  live  load  is: 
3.47  =  2.88  square  inches. 


The  equivalent  flange  area  is  assumed  to  act  at  the  center  of 
gravity  of  the  flange  ;  and  the  bending  moments  equivalent  to  the 
above  areas  are,  for  dead  load; 

0.59  X  20000  X  72.554  =  S5G  000  pound-niches; 
and  for  live  load  : 

2.88  X  10000  X  72.554  =  2  090  000  pound-inches. 


107 


188  BRIDGE  ENGINEERING 

These  bending  moments  must  be  taken  up  by  the  horizontal  splice 
plates      The  stresses  in  these  plates  (see  Fig.  160)  are,  for  dead  load: 

856  000 

-^v— Q--  =  15  /SO  pounds; 

and  for  live  load, 

2  090  000 

—  =  38  500  pounds. 
o4.2o 

While  the  allowable  unit-stresses  are  a  maximum  at  the  center 
of  gravity  of  the  flange  and  are  those  given  by  the  Specifications,  they 
decrease  rapidly  towards  the  center  of  the  girder,  being  zero  at  the 
neutral  axis  of  the  entire  section.  The  unit  allowable  stress  at  the 
center  of  the  horizontal  plates  will  not  be  so  great  as  the  maximum 
allowable,  but  will  be  proportional  to  the  distance  from  center  (see 
Fig.  160).  The  horizontal  plates 'will  be  taken  8  inches  in  width. 
The  unit-stresses  are  easily  determined  by  means  of  the  similar 
triangles  oab  and  006'.  The  dead-load  stress  is  determined  from  the 
proportion : 


207)00 


and  is  14  950  pounds.     For  live  load,  the  unit-stress  will  be  one-half 
of  this  amount,  or  7  475  pounds. 

The  area  required  for  this  plate  is,  for  dead  load,  rr-TT  =    1  ^ 


38  ^00 
square  inches,  and  for  live  load  ~f,^~.  .-  =F  5.16  square  inches,  making 


a  total  of  6.21  square  inches  for  both  plates.     Assuming  two  rivet- 
holes  out  of  the  section,  the  net  width  is  8  —  2  Q  +  -J)  =  6  inches; 

6  ^1 
and  the  required  thickness  for  one  plate  is   -  =  0  .  52,    say   ,06 

i  ~  X  6 

inch. 

The  joint  will  be  weakest  in  bearing  in  the  -jj-inch  web.       The 
number  of  rivets  required  is  : 

15  670+  38  500 


4  920 
The  design  of  the  shear  plate  is  as  fpllows:    The  shear  is  28  COO 

28  600 
pounds,  and  the  required  area  is^nnn    =3.18  square  inches.     As 


010 

the  length  of  the  plate  is  46J  inches,  the  required  thickness  is  —       ^  — 

2.  X  4o.2o 


198 


BRIDGE  ENGINEERING  189 


=  0.034  inch,  but  on  account  of  the  Specifications  it  cannot  be  less 
than  |  inch  thick.  It  will,  however,  be  made  j96  inch  thick,  since 
it  will  then  fill  out  even  with  the  horizontal  tension  plates  and  no 
filler  will  be  required.  Bearing  in  the  web  plate  decides  the  number 
of  rivets,  which  is: 

28600 

"4920  =  °  sh°P  riVetS' 

The  width  of  this  shear  plate  should  be,  as  before,  10  inches.  The 
same  conditions  limiting  the  spacing  of  the  rivets  apply  here  as  in  the 
case  where  the  splice  was  designed  for  shear  only.  The  length  of  the 
horizontal  plates  should  be  sufficient  to  get  in  all  the  rivets,  and  this 
is  a  detail  which  is  left  to  the  judgment  of  the  draftsman. 


f 


1 


-  '«•    Proportion,,  <*****  Bearing  Plate,  and 


PROBLEMS     FOR 
PRACTICE 

1.  A      plate- 
girder  is  87  ft.  9  in. 
center   to    center  of 
end    bearings.     The 
dead-load      moment 

is    9  125  000  pound-          _t  _ 

inches,  and  the  live-      r—  r»  —  ' 

load       moment       is  \ 

38  205  000      pound- 

inches,      the      total 

•shear     at    the     sec- 

tion    being    202  700 

pounds.    The  web  is 

90  by   -.v-inch,    arid 

the  flange  angles  are 

G   by    6    by    |-inch. 

Design   the  web  splice    when  no  part    of    the    web  is  considered  as  taking 

bending  moment. 

2.  For  the  girder  of  Problem  1,  above,  design  the  splice  when  J  of  the 
gross  area  of  the  web  is  considered  as  effective  flange  area. 

77.  The  Bearings.  Articles  113  to  119  of  the  Specifications 
should  be  carefully  studied  before  proceeding;  also  Article  87.  Article 
70  should  be  referred  to,  and  the  remarks  there  made  about  bearings 
should  be  read.  In  case  the  length  of  bearing  is  such  as  to  allow  a 
simple  -2-inch  plate,  care  must  be  taken  that  the  bearing  plate  does 
not  extend  past  the  flange  angles  more  than  2  inches,  or  that  the 
masonry  plate  does  not  extend  past  the  bearing  plate  over  2  inches. 
Reference  to  "Steel  Construction,"  Part  II,  p.  96,  to  Fig.  161, 


109 


100 


BRIDGE  ENGINEERING 


and  to  the  discussion  which  follows,  will  explain  the  reason  of  this. 

I 


=  ~  =  250  X  I  X     0 


_ 

"   12" 


1X9   . 
16  X  12' 


and  as  s  =  10000, 


} 


10000X 


from  which, 

Z  =  1  .94,  say  2  inches. 

In  case  it  is  desirable  to  have  a  simple  masonry  plate  instead  of  a 
cast-steel  pedestal,  and  to  have  the  plate  extend  over  the  sides  of  the 

angles  a  distance 
greater  than  2  in- 
ches, then  some 
arrangement  must 
be  made  for  sup- 
porting the  pro- 
jecting portion. 
Fig.  162  shows  one 
of  the  methods 
most  commonly 
used.  Notwith- 
standing the  brac- 
ing of  the  gusset 
plates,  the  mason- 
ry plate  is  not  ade- 
quately supported, 
the  greater  pro- 
portion of  the 
stress  coming 
upon  the  ends. 

The  disadvan- 
tage of  having  the 
masonry  plate  too 
long  is  plainly 

shown  by  Fig.  163.     Here  the  girder  is  shown  deflected  under  a  live 
load,  the  rear  end  of  the  plate  being  tilted  up  and  the  greater  part 


Pig.  162.    Arrangement  where  Masonry  Plate  is  Used  instead 
of  Cast-Steel  Pedestal. 


200 


BRIDGE  ENGINEERING 


191 


o'f  the  pressure  coming  upon  the  forward  end.     The  use  of  this  style 
of  plate  is  not  to  be  recommended 
for  spans  over  40  feet. 

The  design  for  the  bearing 
of  the  girder  under  consideration 
will  now  be  made.  The  total 
reaction  of  one  girder  must  now 
lx>  computed.  This  will  be  due 
to  the  weight  of  the  steel  in  the 
girder,  to  the  weight  of  the 
track,  and  to  the  reaction  pro- 
duced by  the  E  40  loading  when 
wheel  2  is  directly  over  the  end 
support.  This  reaction  is: 


Btormq  Plate 

Masonry 
Plate 


Fig.  163.    Effect  of  Having  Masonry  Plate 
Too  Long. 


Weight  of  Steel, 


(123.5 


10  X  61 . 75)  61.75 
4 


400 


Weight  of  Track,- ;;      (61.75  +  1.75)$ 
Reaction  Due  to  Engine  Loading 


1 1  430  pounds 

6  350     ' ' 
=    99700     " 


Total 


117  480  pounds. 


The  square  inches  of  bearing  surface  required  is  —  ^— 

2oO 


470; 


and,  as  the  length  is  1  foot  9  inches,  or  21  inches,  the  total  width  of  the 

470 
cast-steel  pedestal  will  be     —  =  22.4,  say  23  inches,  or  1    foot    11 

inches. 

A  bearing  plate  must  be  riveted  to  the  lower  flange  where  it 
rests  upon  the  pedestal.  The  pedestal  must  be  so  constructed  as  to 
allow  this  bearing  plate  to  set  in  it.  Hand-holes  should  be  provided 
in  the  casting  in  order  to  allow  the  bolts  which  connect  the  casting  to 
the  girder  to  be  inserted.  These  bolts  should  be  at  least  f  inch  in 
diameter.  Anchor  bolts  f  inch  thick  and  at  least  8  inches  long  should 
be  provided  and  fox-bolted  to  the  masonry.  The  thickness  of  the 
metal  in  all  parts  of  the  casting  should  be  at  least  \\  inches.  The 
details  of  the  pedestal  are  given  in  Fig.  164,  the  length  of  the  bearing 
being  made  12  inches  so  as  to  allow  one  rivet  to  be  driven  in  the 
flange  angle  in  the  space  between  the  end  stiffeners. 

Allowance  should  be  made  for  a  variation  of  150  degrees  in  tem- 


201 


192 


BRIDGE  ENGINEERING 


perature.  The  coefficient  of  expansion  for  steel  per  unit  of  length  is 
0.0000065,  and  the  amount  of  expansion  for  150  degrees  of  tempera- 
ture will  be : 

0.0000065  X  (61  ft.  9  in.)  X  150  =  0.00  foot. 

This  is  about  f  inch,  and  therefore  the  holes  in  the  flanges  at  one  end 
of  the  girder  should  be  made  oblong  and  long  enough  to  allow  the 


Fig.  164. 


Sido  and  End  Elevations  Showing  Construction  of  Pedestal  and  Connection 
to  Bearing  Plate. 


girder  to  move  4-  inch,  or  |  inch  either  backward  or  forward  from  a 
central  position.  In  determining  the  length  of  this  slotted  hole  (see 
Fig.  If  Jo),  it  must  be  noted  that  the  J-inch  bolt  takes  up  part  of  this 
hole,  and  therefore  its  length  should  be  |  +  $  =  say  If  inches.  The 
width  of  the  hole  should  be  sufficient  to  allow  for  any  over-run  in  the 
diameter  of  the  bolt.  It  should  be  at  least  1  {-  inches  wide. 


PROBLEMS  FOR  PRACTICE 

1.  Determine  the  distance  center 
to  center  of  bearings,  and  the  size 
of   the  masonry  plate,  for  a  plate- 
girder  of  40-foot  span  under  coping, 
the  loading  being  E  40. 

ANS.  41  ft.  4  in.;  350  square  inches. 
(NOTE — Interpolate  values  in  Ta- 
ble I,  Cooper,  p.  80.) 

2.  If  the  girder  span   is  78  feet 
under  coping,  and  the  loading  K  40, 

determine  the  maximum  end   reaction  and  the  width  of  the  masonry 
plate.  ANS.     147  130  pounds;  24 \  inches. 

78.    The  Stress  Sheet.    Plate  II  (p.  1 72)  shows  the  stress  sheet  for 


Fig.  1(55.  Slotted  Bolt-Hole  in  Flange  at 
End  of  Girder  to  Allow  for  Contraction  and 
Expansion  Due  to  Temperature  Changes. 


BRIDGE  ENGINEERING  193 

the  girder  which  has  just  l>een  designed.  It  represents  the  best  modern 
practice  in  that  it  gives,  in  addition  to  the  sizes  of  all  the  sections, 
the  curves  for  the  maximum  shears  and  moments,  the  rivet-spacing 
curve,  and  the  number  of  rivets  required  in  the  different  parts  of  the 
structure.  This  general  form  has  been  adopted  by  one  of  the  largest 
bridge  corporations  in  this  country,  and  is  to  be  recommended  since 
it  gives  the*  draftsman  all  necessary  data  and  thus  prevents  the  loss 
of  time  by  an  inexperienced  man  in  recomputing  certain  results.  The 
results  just  referred  to  are  the  shears,  the  moments,  the  rivet  spacing, 
and  the  number  of  rivets  required  in  the  various  parts.  Formerly  it 
was  not  customary  to  give  this  information  on  the  stress  sheet,  and 
the  draftsman  was  therefore  required  to  do  all  this  computation  which 
had  previously  been  worked  out  by  the  designer  but  had  not  been 
placed  on  the  stress  sheet  in  available  form,  and  thus  unnecessary  loss 
of  time  resulted. 

DESIGN  OF  A  THROUGH  PRATT  RAILWAY=SPAN 

79.  The  Masonry  Plan.  The  same  remarks  which  are  made 
in  Article  67  apply  here.  In  this  case  the  length  of  the  masonry  plate 
is  usually  determined  by  considerations  relative  to  the  number  and 
length  of  the  rollers  in  the  bearing,  and  not  by  the  bearing  per  square 
inch  upon  the  masonry,  the  size  of  the  plate  as  determined  by  the 
above  considerations  being  usually  much  larger  than  if  it  had  been 
determined  by  the  unit  bearing  stress.  A  preliminary  design  of  the 
masonry  plate  is  usually  made  in  a  manner  similar  to  that  done  in  the 
case  of  the  plate-girder;  or  the  length  of  the  masonry  plate  may  be 
approximately  determined  from  the  following: 


LENGTH  OF  MASONRY  PLATE 

FIXED  END 

ROLLER  END 

100  feet 

23  inches 

23  inches 

125  " 

2G     " 

26       " 

150  " 

28     " 

28       " 

175  " 

31      " 

31        " 

200  " 

35 

35 

The  above  masonry  plates  are  for  single-track  bridges,  with  or  with- 
out end  floor-beams,  the  length  being  the  same  in  either  case. 


194  BRIDGE  ENGINEERING 

80.  Determination  of  the  Span.    The  determination  of  the  span 
is  made  in  exactly  the  same  manner  as  described  in  Article  68.     Care 
should  be  taken,  in  case  end  floor-beams  are  not  used,  to  allow  for 
the  pedestal  stones,  which  are  square  stones  resting  directly  upon  the 
bridge  seat,  and  upon  the  top  of  which  rest  the  masonry  plates  of  the 
stringers.     Their  height  must,  of  course,  be  such  as  to  keep  the 
stringers  level.     In  case  these  stones  are  used,  their  size  must  be 
determined;  and  if  it  is  greater  than  that  of  the  bearing  or  masonry 
plates,  then  their  size  determines  the  width  of  the  bridge  seat  and 
the  span  center  to  center  of  bearings. 

81.  The  Ties.     In  the  design  of  the  ties,  as  well  as  in  all  the 
design  which  follows,  the  Specifications  of  the  American  Railway 


i 


Fig.  166.    Spacing  of  Stringers  and  Rails,  and  Position  of  Loads. 

Engineering  &  Maintenance  of  Way  Association  will  be  followed. 
Whenever  reference  is  made  to  these  specifications,  the  number  of 
the  article  will  be  enclosed  in  parentheses,  as  "(£>)/'  which  signifies 
that  Article  5  of  the  Specifications  is  to  be  referred  to. 

The  stringers  in  the  bridge  in  question  will  be  taken  6  ft.  6  in. 
center  to  center.  The  maximum  loading  (7)  is  such  as  to  bring 
8  333  pounds  on  one  tie,  and  to  this  must  be  added  100  per  cent  for 
impact,  making  a  total  of  16  667  pounds.  In  order  to  illustrate  the 
method  of  assuming  the  distance,  center  to  center  of  rails,  as  5  feet, 
that  distance  will  be  used  in  this  case.  The  maximum  moment  will 
then  be  9  X  16  667  =  say,  150  000  pound-inches.  The  size  of  the 
tie  will  be  determined  as  in  Article  71,  the  allowable  unit-stress 
being  2000  pounds  per  square  inch  (5).  If  a  7  by  9-inch  tie  is 
used,  the  unit-stress  will  be  1  590  pounds.  If  a  6  by  8-inch  tie  is 
used,  the  unit-stress  will  be  2  340  pounds.  It  is  evident  that  a  7 
by  9-inch  tie  must  be  used.  See  Fig.  166  for  spacing  of  stringers  and 


204 


BRIDGE  ENGINEERING  195 

rails,  and  for  position  of  the  loads.  Note  that,  although  impact 
is  taken  into  account  in  this  case,  the  size  of  the  tie  is  the  same  as 
that  designed  for  the  plate-girder,  although  the  unit  allowable  stress 
also  differs. 

82.  The  Stringers.  The  width,  center  to  center  of  trusses,  will 
be  assumed  as  17  feet,  since  this  is  sufficient  to  clear  the  clearance 
diagram  in  cases  of  single-track  bridges  of  spans  less  than  250  feet. 

The  span  which  is  to  be  designed  in  the  following  articles  is  a 
through-Pratt  with  7  panels  of  21  feet  each,  making  a  total  span,  center 
to  center  of  bearings,  of  147  feet  0  inches.  See  Plate  HI  (p.  251) .  Rivets 
I  inch  in  diameter  will  be  used  throughout,  except  in  channel  flanges. 

The  length  of  the  stringers  end  to  end  will  be  21  feet,  and  accord- 
ing to  Cooper's  Specifications/  p.  32,  the  maximum  moment  for  the 
live  load  will  be  226000  pound-feet  per  rail.  The  coefficient  of 

impact  (9)  will  be  (  —   — 5x77)  =  0.935,  and  therefore  the  moment 
>  21  -|-  oOO  ' 

due  to  impact  will  be  0.935  X  226000  X  12  =  2535000  pound- 
inches,  making  a  total  of  5  247  000  pound-inches  due  to  live  load. 

The  section  modulus  for  any  particular  beam  is  equal  to  the 
bending  moment  divided  by  the  unit-stress,  and  this  is  equal  to  the 
moment  of  inertia  divided  by  one-half  the  depth  of  the  beam.  This 
latter  quantity  is  constant  for  any  given  beam,  and  for  I-beams  may 
be  found  in  column  11,  Carnegie  Handbook,  p.  98. 

On  account  of  the  cheapness  of  I-beams,  they  will  be  used  for 
stringers  in  this  bridge;  and  sufficiently  heavy  shelf  angles  will  be  used 
to  take  up  any  distorting  influences  due  to  the  eccentric  connections 
which  are  unavoidable  in  this  case.  In  case  an  I-beam  had  not  been 
decided  upon,  the  stringers  would  have  been  small  plate-girders  with 
a  span  of  21  feet  and  depth  according  to  formula?  given.  They  would 
have  been  computed  in  exactly  the  same  manner  as  a  plate-girder 
span  of  21  feet  center  to  center  of  bearings. 

Since  the  dead-load  moment  cannot  be  determined  until  the  size 
of  the  stringer  is  known,  an  approximate  design  must  first  be  made 
by  using  the  live-load  bending  moment  alone;  and  then,  with  the 
size  determined  in  this  manner,  the  extra  section  modulus  required 
for  the  dead-load  moment  due  to  the  weight  of  the  beam  and  the 
track  must  be  computed.  If  this  extra  section  modulus,  added  to  the 
one  previously  determined,  is  greater  than  that  given  by  the  beam  in 


205 


196  BRIDGE  ENGINEERING 

question,  a  larger  size  beam  must  be  used  and  a  recomputation  made. 

5  247  000 
The  section  modulus  (17)  required  for  live  load  only  is  — 

10  UUU 

=  327.9.  As  this  is  too  large  for  one  beam,  two  beams  will  be  used, 
thus  giving  a  required  section  modulus  of  164  for  one  beam.  Two 
24-inch  80-pound  I-beams  will  be  used,  giving  a  total  section  modulus 
of  2  X  174  -  348. 

Assuming  the  rails  and  ties  to  weigh  400  pounds  per  linear  foot, 

400 
the  dead  load  per  linear  foot  per  stringer  is  80  +  =  180  pounds. 

The  dead-load  moment  is  therefore  -  =119  000 

pound-inches.     This    requires    an    additional    section    modulus    of 

119  000 

— •=  7.45.     This,  added  to  the  164  as  determined  above,  makes 
16  000 

a  total  required  section  modulus  of  171.25,  which,  being  less  than 
174  (which  is  that  for  one  I-beam),  indicates  that  the  above  chosen 
beam  is  sufficient  in  strength,  and  it  will  therefore  be  used. 

The  number  of  rivets  in  the  end  connections  will  now  be  deter- 
mined. The  total  end  reaction  for  one  I-beam  is  equal  to  the  weight 
of  one-half  the  beam,  one-eighth  the  track  in  the  panel,  and  one-half 
the  maximum  live-load  reaction  for  one  rail.  These  quantities  are: 

\  Live-Load  Reaction  =  — ^ — =  25  700  pounds. 

Impact  =  25  700  X  0.935 =24  030      " 

400         °1 
Weight  of  Track  =    ^  X  ~9    =       530      " 

Weight  of  Stringer  =    ~    X  80 =       840      " 


Total  =  51  100  pounds. 
The  coefficient  of  impact  is  that  for  a  loaded  length  of  21  feet. 

From  p.  177,  Carnegie  Handbook,  sixth  column,  it  is  seen  that 
the  longest  connection  angle  which  can  be  used  with  a  24-inch  I-beam 
is  20f ,  say  20  inches.  In  this  case  the  thickness  of  the  connection 

angles  must  be —  =  0.23  inch;  but  according  to   (36),  f 

10  000  X  22 

inch  will  be  used.  The  angles  chosen  will  be  6  by  3£  by  f-inch. 
The  6-inch  leg  will  be  placed  against  the  web  of  the  floor-beam  in 
order  to  allow  for  sufficient  room  for  rivets  to  be  driven. 


2oe 


BRIDGE  ENGINEERING  197 


The  rivets  will  tend  to  shear  off  at  places  between  the  webs  of 
the  stringer  and  floor-beam  and  the  connection  angles.  They  will 
also  tend  to  tear  out  of  the  web  of  the  stringer  and  out  of  the  web  of 
the  floor-beam.  As  the  thickness  of  this  latter  is  not  known,  the 
determination  of  the  rivets  for  this  condition  will  be  made  under  the 
next  article.  The  bearing  value  of  a  |-inch  rivet  in  a  |-inch  plate 

(19)  is  1  X  ^  X  24  000  -  10  500  pounds,  and  therefore  ~]        =  5 

lu  ouu 

shop  rivets  are  required  in  bearing  in  the  web  of  the  stringer.  The 
value  of  a  |-inch  shop  rivet  in  single  shear  (18)  is  0.6013  X  12  000  - 
7  220  pounds,  and  the  number  of  rivets  required  to  prevent  shearing 

,    .  51  100 
between  the  connection  angles  and  the  webs  is  -=~^.  =  7  shop  rivets. 

/    __'  ' 

The  value  of  a  f-inch  field  rivet  in  single  shear  (18)  is  0 . 6013  X  1 0  000 

=  6  013  pounds,  and  therefore  —          =9  field  rivets  are  required  to 

b  OJ  o 

connect  the  connection  angle  to  the  web  of  the  floor-beam.     As  men- 
tioned above,  the  number  of  rivets 
in  bearing  in  the  web  of  the  floor- 
beam  will  be  determined  in  the     K/9  Field 


next  article;  and  if  the  number 
required  for  bearing  is  greater 
than  9,  then  that  number  must 
be  used  instead  of  9.  Fig.  167 
shows  the  connection  of  the 
stringer  to  the  floor-beam  web, 
and  also  the  number  of  rivets  as 
determined  above,  in  their  proper 


7  Shop 


/I-beam  W«b 


Floor  Beam  Web 


/I-beam  Web 


F5Kop 
Id 


positions.    The  distance  between      Fig.  1 67.    Connection  of  Stringer  to  Floor- 
,  »     ,  .  Beam  Web ;  also  Number  of  Rivets. 

the  webs  ot  the  stringers  must 

be  such  as  to  prevent  their  flanges  from  touching  at  the  top. 

The  stringers  should  be  connected  at  the  bottom  by  a  system  of 
lateral  bracing  of  the  Warren  type.  The  size  of  these  angles  cannot 
be  determined  by  theoretical  considerations,  but  is  usually  chosen  to 
be  3|  by  3^  by  f-in.  See  Plate  II  (p.  172)  for  the  general  arrangement 
of  this  bracing. 

83.  The  Floor=Beams.  All  floor-beams  should  be  of  sufficient 
depth  to  allow  the  use  of  small-legged  connection  angles  at  the  ends 


198  BRIDGE  ENGINEERING      • 

where  they  join  the  end-posts.  The  thickness  of  the  web  should  also 
be  greater  than  that  which  is  theoretically  computed,  in.  order  that 
sufficient  bearing  may  be  given  so  that  the  rivets  for  the  stringer 
connections  will  not  require  the  stringers  to  be  of  too  great  a  depth. 
The  depth  of  the  floor-beam  will,  of  course,  vary  somewhat  with  the 
length  of  the  panel  and  with  the  loading,  but  should  not  be  less  than 
36  inches  in  any  case.  A  considerable  variation  in  the  depth  will 
not  affect  the  weight  of  the  floor-beam  or  the  bridge  to  an  appreciable 
extent.  A  good  plan  is  not  to  exceed  a  depth  of  5  feet,  with  panel 
lengths  of  25  feet  and  E  50  loading.  In  this  bridge  the  depth  of  all 
intermediate  floor-beams  will  be  taken  as  48  inches.  It  is  good 
practice  not  to  consider  |  the  web  area  when  designing  flanges  of 
floor-beams  and  stringers,  and  the  design  here  given  does  not  consider 
the  web  as  taking  any  bending  moment. 

The  design  of  an  intermediate  floor-beam  will  now  be  made. 
The  loads  for  which  it  is  designed  are  the  floor-beam  reaction  due  to 
the  live  load  (see  Cooper,p.  32),  the  floor-beam  reaction  due  to  impact, 
the  dead  weight  of  the  stringers  and  track,  and  the  weight  of  the  beam 
itself.  The  latter  weight  is  distributed  uniformly  over  the  entire 
length  of  the  beam,  and  the  other  loads  act  as  concentrated  loads 
spaced  6  feet  6  inches  apart  at  equal  distances  from  the  center. 
The  computation  of  the  concentrated  loads  is  as  follows: 

Live  Load  =  ....................  ........  68  000  pounds 


Impact  =  68  000  X  (  Q7 

o  t    ~r 


oUU 


60  500 


Dead  Load  of  Stringer  =  2  (  21  X  ^  --  8°  )  .  .      3  320 

400 
Dead  Load  of  Track  =  -  ---  —  X  21  .........      4  200- 


Total  =  136  020  pounds. 

The  moment  at  points  under  the  loads  (see  Fig.  168)  is  136  020 
X  5.25  X  12  =  8  575  000  pound-inches.  This  is  due  .  to  the  con- 
centrated loads  only.  The  weight  of  one  floor-beam  may  be  approxi- 
mately determined  by  the  same  formula  as  used  to  determine  the 
weight  of  plate-girder  spans;  only,  in  place  of  the  length  of  the  span, 
the  length  of  the  panel  must  be  substituted.  The  total  weight  of  the 
above  floor-beam,  then,  is: 

TF  =  0.45  X  (123.5  +10  X  21)  X  21  =  3  160  pounds. 


BRIDGE  ENGINEERING 


199 


The  dead-load  moment  at  the  center  due  to  this  weight  will  be: 

Wl        3  160  X  17  X  12 

—  =  80  700  pound-inches, 

O  O 

making  a  total  moment  at  the  center  of  the  beam  of  8  575  000  +  80  700 


<0 

2 

i 

I 

i    i 

^              5'-  3" 

c                     6""6"                    j. 

1             5'-3M 

17-0" 

Fig.  168.    Diagram  Showing  Loads  on  Floor-Beam. 

=  8  655  700  pound-inches.     Note  that  the  dead-load  moment  at  the 

center  of  the  beam  is  added  to  the  concentrated-load  moment  at  the 

point  where  the  concentrated  load  is  applied.     This  will  give  the 

total  moment  at  the  center  of  the  beam  as  shown  by  Fig.  169,  since 

the  concentrated-load  moment,  is 

constant   between  the  points  of 

application.     The   end    shear -is 

readily  computed  to  be  136020 

+  1  580  =  137  600  pounds.    The 

curves  of  moments  and  shears  are 

shown  in  Fig.  169. 

The  total  depth  of  the  floor- 
beam,  back  to  back  of  angles,  is 


.rf  Center  toCcnUr 


Fig.  169.    Shear  and  Moment  Diagram. 


48  j  inches ;  and  the  effective  depth 
will,  for  approximate  computa- 
tion of  the  flange  area,  be  taken  as  somewhat  less,  say  44^  inches, 
since  the  flange  angles  will  probably  be  6  by  6-inch  and  the  center 
of  gravity  of  most  of  these  angles  lies  about  If  inches  from 

8  655  700 


the  back.     The  approximate  flange   stress  is 
pounds,     and     the    required     net    area     (17) 


44.5 
will  be 


=  194  500 
194  500 
16000 


200 


BRIDGE  ENGINEERING 


=  12.2  square  inches.  In  assuming  the  size  of  the  angle,  it  is  to  be 
remembered  that  when,  as  in  this  case,  no  cover-plates  are  used,  no 
rivet-holes  will  be  taken  out  of  the  top  flange,  and  only  one  rivet- 
hole  will  be  taken  out  of  the  vertical  flange. 

Two  j6  by  6  by  f -inch  angles  give  a  gross  area  of  7.11  square 
inches  each,  and  a  net  section  of  7 . 1 1  —  0 . 625  =  6 . 485  square  inches 
each,  or  12 . 97  square  inches  net  for  both.  As  this  is  near  the  required 
area,  these  angles  will  be  taken;  and  a  recomputation  will  now  be 
made  with  the  actual  effective  depth,  in  order  to  see  if  sufficient 
variation  in  the  areas  occurs  to  require  another  angle  to  be  taken. 
The  actual  effective  depth  is  now  48}  —  2  X  1 .84  =  44. 57  inches; 
and  making  computations  with  this,  it  will  be  found  that  a  net  area 
of  12.10  square  inches  is  required.  As  this  is  practically  the  same 

as   was   determined   at  first,  no 


75KO        I 

Li  i  Field 

|/7ShOp 

change  will  be  made  in  the  size 
of  the  angle. 
The    web    is    to   be  designed 
for    a    total    shear   of    137600 
pounds.  The  required  area  (18)  is 

137  600 
—  lo  7b  souare  inches 

?"  Web  of  I-beam^ 
fl  a*  Web  ot  I-beam;, 

^^RJ 

7  Shop-'    fc: 

I 

F5hop 
Ft  eld 

/Floor  Beam  Web 

10000 
and    the    required    thickness    is 

Pis.  170.    Calculation  of  Number  of  Rivets  UIK>  <ou,, 

through  Connection  Angles  of  Stringer  3  •      u    mn^    Up    n<,pr]        Thp  wpb 

and  Floor-Beam  Web.  USCU. 

will  accordingly  be  48  by  f-inch. 

The  determination  of  the  number  of  rivets  which  go  through  the 
connection  angle  of  the  stringer  and  the  web  of  the  floor-beam  can 
now  be  made.  The  value  of  a  f-inch  field  rivet  in  bearing  in  a  f-inch 
plate  (19)  is  |  X  |  X  20  000  =  6  560  pounds,  and  the  total  number 

.     ,  .  136020 

required  in  one  connection  angle  will  be  - —  =  11  field  rivets 

2 X  b  5bO 

(see  Fig.  170). 

The  pitch  of  the  rivets  in  the  flange  can  in  this  case  be 
determined  by  the  use  of  the  formula: 

vh. 


210 


BRIDGE  ENGINEER IXG  201 

Since  the  flange  is  of  the  same  cross-section  throughout,  the  value 
of  the  effective  depth  will  not  change,  and  it  can  therefore  be  used  in 
the  above  equation  instead  of  considering  the  value  of  the  distance 
between  rivet  lines.  The  shear  being  practically  constant  from  the 
connection  of  the  stringers  to  the  end  of  the  floor-beams,  the  rivet 
spacing  will  be  constant  in  this  distance.  It  will  be: 

7  880  X  44 .  57 

137600          =2.  finches, 

the  value  of  a  f-inch  shop  rivet  in  bearing  in  the  f-inch  web  being 
|  X  |  X  24  000  =  7  880  pounds.  This  is  seen  to  be  less  than  2| 
inches;  but,  as  the  angles  have  6-inch  legs,  this  spacing  can  be  used  in 
a  horizontal  direction ;  and  the  distance  from  center  to  center  of  rivets, 
which  will  be  placed  in  rows  on  two  gauge  lines,  will  still  be  greater 
than  2|  inches. 

The  shear  between  the  stringer  connections  is  practically  zero, 
and  therefore  the  spacing  will  be  very  large.  Being  over  6  inches,  it 
will  be  subject  to  (37). 

The  connection  angles  at  the  ends  of  the  floor-beams  will  be 
taken  as  6  by  3^  by  f-inch,  the  6-inch  legs  being  against  the  web  of 
the  floor-beam.  The  other  legs  are  chosen  small  in  order  that  they 
may  fit  into  the  channels  which  will  very  likely  be  required  for  the 
posts;  and  according  to  the  sixth  column,  p.  183,  Carnegie  Handbook, 
only  8}  inches  is  available  for  this  purpose.  This  8J  inches  is  taken 
from  a  10-inch  channel,  since  this  is  the  smallest  channel  that  can  be 
used  which  will  give  room  for  connection  and  yet  be  in  accordance 
with  the  Specifications.  This  is  due  to  the  fact  that  its  web  (36)  is 
greater  than  f  inch.  The  rivets  which  connect  the  end  angles  to  the 
floor-beam  web  are  shop  rivets,  and  those  which  connect  the  end 
angles  to  the  posts  are  field  rivets.  Since  the  size  of  the  post  is  not 
known,  the  thickness  of  its  metal,  of  course,  cannot  lie  used,  and 
therefore  the  number  of  rivets  required  in  bearing  in  the  post  cannot 
be  determined  at  this  time. 

The  number  of  shop  rivets  required  through  the  end  angles 
and  the  floor-beam  web  is  governed  by  the  bearing  of  the  rivets  in  the 
f-inch  web  of  the  floor-beam.  The  value  of  a  f-inch  shop  rivet  in 
bearing  in  a  f-inch  web  (19),  as  has  just  been  computed,  is  equal  to 

1 37  600 
7  880  pounds,  and  the  number  of  rivets  required  is =  18. 


211 


202 


BRIDGE  ENGINEERING 


The  number  of  field  rivets  required  in  single  shear  to  connect 

An  even  number  of 


the  end  angles  with  the  posts  is  —        —  =  23. 

D  Olo 


Weft  ot  FlooT 
r  Beam 


rivets  will,  of  course,  have  to  be  used,  one-half  going  into  each 
of  the  3^-inch  legs.  See  Fig  171  for  the  position  and  the  number 
of  rivets.  It  must  be  remembered  that  more  than  these  num- 
bers may  be  used  by  the  draftsman  on  account  of  rivet  spa- 
cing which  may  be  required  by 
conditions  other  than  those  of 
design. 

The  design  of  the  end  floor- 
beam  is  somewhat  different  from 
that  of  the  intermediate  floor- 
beams  in  that  the  load  which 
comes  upon  it  is  considerably 
lighter,  since  this  floor-beam 
takes  the  dead  load  of  only  one- 
half  the  panel  and  the  live  load 
due  to  the  maximum  end  reaction 
for  a  stringer  length  instead  of 
the  floor-beam  reaction  for  the 
stringer  length  (see  Cooper,  p. 
32). 

The  maximum  end  shear  is  computed  as  follows: 
End  Shear  for  21-foot  Span    51  400  pounds. 


Channel  of 

>05t 


Fig.  171.    Position  and  Number  of  Rivet 
to  Connect  End  Angles  with  Posts. 


Impact  =  51  400  X 


300 


Dead  Load  of  Stringers  = 


300, 

BO  X  2  X  21 


Dead  Load  of  Track  = 


48  000 


1  6SO 


2  100 


Total     103  ISO  pounds. 

The  maximum  moment  due  to  the  above  load  is  103  180  X  5.25 
X  12  =  6  500  000  pound-inches.  The  weight  of  the  beam  may  be 
assumed  as  3  160  pounds.  This  is  the  same  as  was  computed  for  the 
intermediate  floor-beam,  but  will  be  used  for  this  beam,  since  the  size 
of  the  web  will  be  the  same  as  in  the  others;  and,  although  the  flange 
area  will  be  less,  the  end  connections  will  be  somewhat  heavier  owing 
to  the  connection  of  the  beam  to  the  end-post  and  the  roller  bearing, 


212 


BRIDGE  ENGINEERING  203 

and  this  additional  weight  will  cause  the  total  weight  of  the  end 
floor-beam  to  be  about  the  same  as  that  of  the  intermediate  ones. 
The  total  moment  at  the  center  will  then  be  6  500  000  +  80  700  = 
6  580  700  pound-inches. 

The  depth  of  the  end  floor-beam  will  be  somewhat  greater  than 
the  depth  of  the  intermediate  floor-beams.  This  is  due  to  the  fact 
that  it  extends  downward  a  greater  distance,  resting  upon  the  bearing 
plate,  which  comes  directly  upon  the  top  of  the  rollers.  The  exact 
depth  cannot,  of  course,  be  determined  until  after  the  roller  bearings 
are  designed;  but  it  may  be  safely  assumed  as  four  or  five  inches 
deeper  than  the  intermediate  floor-beams,  and  in  case  this  is  not 
enough,  the  draftsman  can  easily  fill  in  the  remaining  distance  with 
filler  plates,  as  this  distance  will  not  be  very  great.  In  case  this  depth 
is  too  great,  the  flange  angles  may  be  bent  upward  at  the  end,  or  a 
re-design  may  be  made. 

The  depth  will  be  assumed  as  52  inches  in  this  case.  The 
effective  depth  will  be  assumed  as  48  inches,  and  this  gives  an  approxi- 
mate flange  stress  of 

658°70°    =137  000  pounds, 

•±O 

and  an  approximate  net  flange  area  required  of 

137  000 
..-  _   „    =  8.57  square  inches. 

A  6  by  6  by  -^ -inch  angle  gives  a  gross  area  of  5.06  square 
inches,  and  a  net  area  of -5.06  —  (f  +  |)  r7T  =  4.62  square  inches. 
A  recomputation  with  the  true  effective  depth  requires  8.42  square 
inches  net.  Two  of  these  angles  give  9.24  square  inches;  and  as  this 
coincides  very  closely  with  the  required  area,  it  will  be  used:  The 
size  of  the  web  plate  is  52  by  f-inch. 

The  pitch  or  spacing  of  rivets  in  the  flanges  is: 

7  880  X  48 

IMW  =  3  62lnches- 

The  maximum  end  shear  as  above  computed  is  taken  by  two 
stringers;  and  therefore  the  number  of  rivets  required  in  bearing  to 
form  the  connection  between  the  stringers,  connection  angles,  and 
the  floor-beam  web  is,  for  each  angle: 

104  760 

2,-^sTr  =  8  field  rivets. 


2  X  6  560 


213 


204  BRIDGE  ENGINEERING 

The  value  6  560  in  the  above  equation  is  the  value  of  a  f-inch  field 
rivet  in  bearing  in  the  f-inch  web. 

The  number  of  rivets  required  in  the  end  angles  on  the  floor- 
beam  is  : 

104  760 

-788F  =  14sh°Prlvets- 

These  rivets  go  through  the  web  of  the  floor-beam.  The  connection 
of  the  floor-beam  to  the  end-post  is  made  by  means  of  field  rivets  and 
a  large  gusset  plate.  This  gusset  plate  is  usually  f  inch  in  thickness. 
The  number  of  rivets  through  the  end  connection  angles  and  this 
gusset  plate  is  governed  by  single  shear,  since  the  rivets  will  shear  off 
between  the  angles  and  the  gusset  plate  before  they  will  tear  out  of 
the  gusset  plate,  as  the  value  of  a  rivet  is  greater  in  bearing  than  in 
shear.  The  number  required  is: 


The  general  arrangement  of  the  intermediate  floor-beams  is 
shown  in  Fig.  172.  The  ends  of  the  lower  flange  are  bent  up  as 
shown,  in  order  to  allow  the  I-bar  heads  or  any  other  section  of  the 
lower  chord  to  have  clearance.  This  makes  it  necessary  for  the  floor- 
beam  web  to  be  spliced  at  the  ends,  as  shown.  The  distance  which 
this  plate  should  extend  above  the  floor-beam  proper  depends  upon 
the  distance  which  the  lower  chord  is  bent  up.  In  any  case  the  length 
of  the  connection  on  the  post  should  be  at  least  equal  to  the  depth 
of  the  floor-beam.  Two  splice  plates,  one  on  either  side  of  the  web, 
are  placed  here  in  a  manner  similar  to  that  of  a  splice  as  designed  in 
the  plate-girder  when  shear  only  was  considered.  Here  shear  only  is 
considered,  and  the  number  of  rivets  which  must  be  on  each  side  of 
the  splice  will  be: 

137  640 

~7~880~  =  P  " 

The  7  880  which  occurs  in  the  above  equation  is  the  value  of  a  f-inch 
rivet  in  bearing  in  a  f-inch  plate  (19).  Inspection  of  Plate  II  (p. 
172)  will  make  this  design  clearer.  Plate  II  also  shows  the  shape  of 
the  end  floor-beams. 

The  small  shelf  angle  shown  in  Fig.  172  should  have  sufficient 
rivets  to  prevent  any  twist  of  the  stringers  due  to  their  being  con- 
nected on  one  side  of  their  web  only.  This  number  is  a  matter  of 


214 


BRIDGE  ENGINEERING 


205 


judgment.  Experience  seems  to  indicate  that  enough  rivets  to  take 
up  one-third  of  the  total  reaction  of  the  stringers  will  be  sufficient. 
This  will  require  shop  rivets,  and  the  number  will  be : 

103  180  ' 
3X7  220  =  P  nve     m  smSle  shear. 

84.     The  Tension  Members.     Tension  members  usually  consist 
of  long,  thin,  flat  plates  with  circular  heads  forged  upon  their  ends. 


Pig.  17S.     General  Arrangement  of  Rivets,  Splices,  Connections,  etc.,  for  Intermediate 
Floor-Beams. 

These  circular  heads  have  holes  punched  through  their  centers  and 
then  very  carefully  bored.  Through  these  holes  are  run  cylindrical 
bars  of  steel  called  pins.  These  pins  connect  them  with  other  mem- 
bers of  the  truss.  See  Carnegie  Handbook,  p.  212,  for  table  of  I-bars. 
The  I-bars  given  are  standard  I-bars ;  and  while  departures  from  these 
widths  and  minimum  thicknesses  may  be  made,  it  may  be  done  only 
at  great  cost  to  the  purchaser.  Note  that  there  are  no  standard 
9-inch  I-bars.  The  thicknesses  given  are  the  minimum  thicknesses 


215 


206  BRIDGE  ENGINEERING 

for  that  width  of  bar,  and  do  not  indicate  that  thicker  bars  of  that 
width  cannot  be  obtained;  but  on  the  contrary  thicker  bars  of  that 
width  can  be  obtained,  and  this  should  be  done,  the  minimum  thick- 
ness as  given  in  the  table  being  avoided  if  possible. 

It  has  been  found  that  bars  which  have  a  ratio  of  thickness  to 
width  of  about  one-sixth  give  good  service  and  are  easy  to  forge. 
This  relation  gives  us  a  rough  guide  which  will  enable  us  to  determine 
the  approximate  width  and  thickness  of  any  bar  of  a  given  area. 
Once  the  approximate  dimensions  are  determined,  the  actual  dimen- 
sions can  be  chosen  from  the  market  sizes  of  the  material  (see  Car- 
negie Handbook,  pp.  245  to  250). 

An  expression  for  the  approximate  de,pth  of  the  bar  will  now  be 
derived  by  using  the  above  relation. 

Let  A  =  Area  of  bar,  in  square  inches; 

d  =  Width  of  bar,  in  inches; 

t  =  Thickness  of  bar,  in  inches. 
Then, 

also, 


Substituting  the  value  of  t  in  the  expression  for  A,  there  results: 
d  =  VGA. 

The  stresses  in  all  the  members  in  the  truss  under  consideration 
are  computed  by  the  method  described  in  Part  I,  and  are  placed  on 
the  stress  sheet,  Plate  III  (p.  251).  In  the  succeeding  design,  the 
student  should  obtain  his  stresses  from  Plate  III  without  his  attention 
being  again  called  to  the  matter. 

Table  XXIV  gives  the  tension  members  and  their  dead-load, 
live-load,  impact,  total,  and  unit  stresses  (15),  together  with  the 
required  area,  the  number  of  bars,  the  approximate  depth  of  bars, 
and  the  final  sizes  used. 

The  first  seven  columns  in  Table  XXIV  are  self-explanatory. 
The  number  of  bars  to  be  used  in  any  particular  case  is  a  matter  of 
judgment.  One  fast  rule  is  that  an  even  number  of  bars  should 
always  be  used,  except  in  the  case  of  counters,  where  one  is  permis- 
sible. This  is  due  to  the  fact  that  the  placing  of  one  of  the  main 
members  in  the  center  of  the  pin  would  create  a  large  moment,  and 


216 


BRIDGE  ENGINEERING 


207 


' 

*         §0 

isy 

03 

:    :3S?§§§§ 
:    :  oi  ^-i  o  o  t^  co 

i 
eS 

0 

therefore  an  ex- 
cessively large  pin 
would  be  required, 

0* 

-       •    ffconjoo                 H« 

A 

and  accordingly  a 

is 

#> 

'.      1    X    X    X    X    X    X 

|«|» 
•       •    t^   ,-(    CD    CO    O    •* 

5 

very  large  head  on 
the  I-bar  in  pro- 

^ 

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i. 

^3 

•    Tf      •    O    "3  O   O 
•    Tf<        •    O    O5    1C    CO 

:    :  t>i   ;  «o  >o  <o  •* 

>• 
5b 
£ 

0) 
^2 
S 

portion  to  its  width 
—  all  of  which  are 
very  undesirable 

AREA*; 
ONK  BAH 

•       •    <M    iM    03    O    1C    » 
•       .    W    CD    Oi    05    0    0 
|       I    OS    r-I   1C    1C   t>^   CO 

ID 

S 

•  1 

-£ 

and  costly.  In  gen- 
eral the  number  of 

§s 

l« 

i       !    <N    i—  1    (M    Tf*    **   (M 

£ 

cC 
V 

small  as  possible, 
and  they  should  be 

c 

K% 

TfiCM'lMGOOO'* 
OoO-*«003<O(M-< 

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so  chosen  that  the 

e 

S^ 

(4 

«OOOGO>-(^ifOOOCO 
i—  I           i-H           i-H    <N   <N 

1- 

£ 

widths  of  the  chord 

>    jg 

X     E 

2* 

H 

5 

- 

OOOtOCOCDOCD 

5 

'5 

from  the  ends  to- 
ward the  center  of 

ea    § 

1  i 

the  truss,  and  the 

<     2 

.  | 

H 

O 
H 

¥ 

TJH^H»fllCr-IOC02GO 

COTt<05(NC:i>Tj<O 

(N    1-H     (M              r-<    CO    ^ 

.a  -g 
.s  s 

lit 

I  47 

widths  of  the  diago- 
nals decrease  from 
the  ends  toward  the 
center  of  the  truss. 

a 
1       £ 

00000000 

1  II 
=  '81 

The  area  of  one 

c        •< 

a        M 

OOOCOCO<MCOOt< 
!>;OO<Mlv<M-<t!Tt< 

•c    o  «= 

§  §"i 

rf    .2   S, 
1     •« 

bar  is  obtained  by 
dividing  the  total 

s    3 
3 
> 

rtHOCCOQOiCCOOOTti 
r-iO-^C^OJOO-HiC 

r-l               rt                         1-H     (M 

s  iii  square  inc 

le  above  tab 
ments  of  the 

ber  of  bars  and  also 
by  the  allowable 
unit-stress.  Thus, 

o 

j 

J, 

e 
Q 

§00      -000       • 
o  o     •  o  o  o 
O   05       •   O   TP   o       • 
I-H    CO   t^      .'    Tf    00    (N 
r*H    i-i    TJH       .    (N    CO   CO       . 

1  "  £ 
|  «'3 

^  •£  i" 

1      w    ^ 

S        >     0 

S      o3  ^ 

h^-           02 

for  the  member 
L2U1;  for  example, 
the  required  area 
of  one  bar  is: 

M 

*     ^  'o 

one  IAA 

H 

•4  ts  tS*  S  tT  sq  kf  £3 

^^      ^3 

=    9  22 

H 

S 

Kf  sq    K5    K?  Kf  ^  «4"  4 

1 

square  inches. 

217 


208  BRIDGE  ENGINEERING 


The  approximate  depth  of  this  bar  is  determined  by  taking  the  square 
root  of  6  times  the  area  as  above  determined.     It  is: 


d  =  V  6  X  9 .  22  =  7 . 44  inches. 

As  this  is  nearer  7  than  8  inches,  a  7-inch  bar  will  be  chosen;  and 
looking  in  the  first  column,  Carnegie  Handbook,  p.  248,  for  an  area 
which  will  be  equal  to  or  in  excess  of  9.22,  it  is  found  that  a 
If -inch  bar  satisfies  this  condition,  and  therefore  the  section  of  this 
member  consists  of  two  bars  7  by  If  inches. 

According  to  (80),  the  first  two  sections  for  the  lower  chord  are 
to  be  made  of  built-up  members.  This  requires  that  instead  of 
I-bars  they  are  to  be  made  of  angles  and  plates,  or,  in  case  the  stress  is 
light,  of  channels.  The  depth  of  the  section  is  limited  by  the  size 
of  the  greatest  I-bar  head.  As  the  diameter  of  the  I-bar  head  depends 
upon  the  size  of  the  pin,  it  cannot  of  course  be  determined  accurately 
before  the  pin  is  designed.  It  is  customary  to  assume  the  largest 
head,  and  to  design  the  section  so  as  to  clear  this.  The  size  of  the 
largest  head  for  bars  of  given  width  is  given  in  the  Carnegie  Hand- 
book, p.  212. 

The  design  of  the  member  L0Z/2  will  depend  upon  the  size  of 
the  largest  head  of  the  7-inch  I-bar  of  the  member  U{LV  This  is  17^ 
inches;  and  in  order  that  the  head  may  have  some  clearance,  it  will 
be  necessary  to  add  \  inch  to  the  top  and  the  bottom,  making  a  total 
of  18o  inches.  Since  the  flange  angle,  as  in  the  case  of  plate-girders, 
will  extend  over  the  plate  about  \  inch,  the  plate  itself  may  be  18 
inches  wide  and  still  give  sufficient  clearance. 

The  total  stress  is  234  200  pounds,  and  the  allowable  unit- 
stress  (15)  is  16000  pounds  per  square  inch.  The  required  net 
area,  then,  is: 

234  200 


16  000 


=  14.64  square  inches. 


According  to  the  Specifications,  the  thickness  of  the  plate  cannot  be 
less  than  f  inch.  The  gross  area  of  two  18  by  f-inch  plates  is  13.5 
square  inches,  and  the  gross  area  of  four  3^  by  3^  by  f-inch  angles, 
which  are  assumed  to  be  sufficient,  is  9.92  square  inches,  thus  making 
a  total  gross  area  of  23 . 42  square  inches.  If  5  rivet-holes  are  assumed 
to  be  taken  out  of  each  web,  and  one  rivet-hole  taken  out  of  each 
angle,  this  will  require  a  certain  number  of  square  inches  to  be 


218 


BRIDGE  ENGINEERING 


209 


less 


e-Pb 


or  less 


deducted  from   the  section,  and   this  is  computed   as  follows: 

Out  of  webs,  2  X  5  ({  +  i)   X  |  =  3.75  sq.  in. 
Out  of  angles,  4  (£  +  i)  X  |  .  .   =  1 .50  "     " 

Total  =  5.25  sq.  in. 

The  net  area  of  the  section  is  now  determined  to  be  23 .42  —  5 .25  = 
IS.  17  square  inches.  This  is  somewhat  greater  than  the  required 
net  area,  but  must  be  used,  for  according  to  (39),  these  are  the  smallest 
and  thinnest  angles  that  may  be  used. 

Figs.  173  and  174  show  the  cross-section  and  the  general  detail 
at  L2.  The  width  of  the  member  cannot  be  determined  until  after 
the  section  of  the  end-post  is 
computed,  since  it  must  fit  inside 
of  the  end -post,  the  horizontal 
legs  of  the  angles  being  cut  off  to 
allow  this.  The  end-post,  Arti- 
cle 87,  is  14^  inches  inside.  If  it 
is  assumed  that  all  the  pin-plates 
on  the  end-post  are  placed  on 
the  outside,  and  all  those  at  L0 
on  L0L2  are  on  the  inside,  then 
the  width  of  L0L2,  back  to  back 
of  plates,  must  be  14  -  (2  X  V 
+  2  X  |)  =  12}-  inches  or  less, 
J-inch  clearance  being  allowed 
between  the  sides  of  the  angles  and  the  web  plates  of  the  end-post 
(see  Fig.  173). 

The  total  net  section  through  the  pin-hole  at  L2  (26)  must  be 
1£  X  18.17  =  22. 7  square  inches,  or  11.35  square  inches  for  one 
side.  The  plate  which  is  to  increase  the  section  must  be  on  the  out- 
side, since  the  intermediate  post  U2L2  and  the  two  I-bars  of  member 
UJ^  must  go  inside.  The  gross  width  of  this  plate  is  1 1J  inches  (see 
Fig.  174),  and  the  net  width  is  2w  =  11|  -  5  =  6£  inches.  The 
net  area  through  the  pin  is: 

Two  3J  by  3£  by  f-in.  angles  =  4 . 96  square  inches. 

One  18  by  $-'m.  plate  =  9  -  5  X  i  =  6.50        "  " 

Total          =  11 .46  square  inches 

Since  this  is  greater  than  the  11 .35  required,  no  plate  will  be  necessary 
to  fulfil  (26)  in  this  respect. 


Fig.  173.    Cross-Section  Showing  Construc- 
tion of  Lower  Chord  Member. 


219 


210 


BRIDGE  ENGINEERING 


BRIDGE  ENGINEERING  211 

Sufficient  bearing  area  must  be  provided  at  this  point.  The 
total  stress  is  234  200  pounds,  the  total  bearing  area  required  is 

234  200 

—  =  9.76  square  inches,  and  the  total  thickness  for  one  side  is 
24  000 

'-'—   =  0 . 976  inches.     Since  the  thickness  of  the  web  is  i  inch,  the 
2X5 

pin-plates  must  be  0 . 976  —  0 . 50  =  0 . 476  inch  (say  \  inch)  thick. 
A  |-inch  pin-plate  must  be  used,  and  as  the  total  thickness  of  the 

0  50       234  200 
bearing  area  is  now  1 .00  inch,  this  pin-plate  will  take    '       X— '— — 

=  58  550  pounds.     The  joint  is  weakest  in  shear,  and  will  therefore 

58550 
require-.—  —  =  8  -t-  (say  9)  shop  rivets. 

In  case  it  is  necessary  to  put  the  member  U^  on  the  outer  side 
of  LyL^,  then  the  outer  legs  of  the  upper  angles  must  be  cut  off  to  allow 
U^L2  to  pass.  This  will  decrease  the  section  by  an  amount  (3^  —  f ) 
X  f  =  1  •  20  square  inches.  Considering  the  pin-plate,  which  is 
(18i  -  2  X  3*)  -  i  =  Hi  inches,  the  |  inch  being  allowed  for 
clearance  between  the  edges  of  its  flange  angles,  the  total  net 
section  through  the  pin-hole  on  one  side  will  be: 

One  Angle         3£  by  3£  by  f-in.  =  2.48  square  inches 
One  Cut  Angle  3|  by  3J  by  f-in.  =  1.31      " 
One  Web  (18  -  5)  J  sq.  in.  =6.50      " 

One  Pin-Plate  (11J  -  5)  f  sq.  in.  =  2.34      " 


Total     =  12.63  square  inches. 

This  is  greater  than  11 .35  as  required,  and  is  therefore  safe. 

The  distance  from  the  center  of  the  pin  to  the  end  must  now 
be  determined  (26).  The  total  net  section  of  the  body  of  the  member 
is  18.17  square  inches,  or  9.09  square  inches  for  one  side,  and  the 
thickness  of  the  web  and  the  pin-plate  is  1  inch.  The  distance  from 

the  pin  to  the  end  of  the  member  is  then  -        =9^  inches,  and  the 

distance  to  the  center  of  the  pin  is  9&  -f  -^  =  Hf ,  say  12  inches  (see 

Fig.  174).  Rivets  should  be  countersunk  where  necessary  to  prevent 
interference  with  I-bars.  For  signs,  see  "Steel  Construction,"  Part 
III,  p.  192,  and  Carnegie  Handbook,  p.  191. 


221 


212 


BRIDGE  ENGINEERING 


At  point  L0  of  this  member,  the  pin  is  6^  inches  in  diameter,  and, 
as  previously  mentioned,  the  legs  of  the  angles  are  cut  (see  Fig.  175). 

9.76 
The  total  bearing  area  required  for  one  side  is  —  '-  —  =  4  .  88,  and  the 

4  88 
' 


required   thickness  is 


0  .  781  inch.    Subtracting  the  thickness 


of  the  ^-inch  web  from  this  gives  0.281  inch.     A  pin-plate  f  inch 
thick  must  be  used. 

The  net  area  through  the  pin  (26)  must  be  11  .35  square  inches. 


Fig.  175.    Elevation  and  Section  Showing  Pin  Connection  at  End  of  Truss. 

This  net  area,  remembering  that  the  angle  legs  are  cut  and  therefore 
their  area  is  that  of  a  bar  3-2-  by  f-inch,  computed  for  one  side,  is  as 
follows  : 

Two  Angles,  legs  cut,  3|  by  3£  by  f-in.  =    2  .  62  square  inches 
One  Web  18  X  i  -  6i   X  i  sq.  in.  =     5.88      "  " 

One  Pin-Plate  Hi  X  $  -  Gi  X  f  sq.  in.  =     1  .87      "  " 

Total       10  .  37  square  inches. 

This  shows  the  section  to  be  deficient,  and  the  thickness  of  the  pin- 
plate  must  be  made  $  inch.  This  gives  a  net  area  through  the  pin 
of  11  .62  square  inches. 

The  distance  between  rivet  lines  (see  Fig.  173)  is  17  \  inches, 
and  (44)  the  tie-plates  must  be  17J  (say  18)  inches  long,  and  their 
1  7 


thickness 


50 


0.346  inch  (say  f  inch). 


BRIDGE  ENGINEERING 


213 


The  lattice  bars  (45)  must  be  2£  inches  wide,  and  (47)  must  be 
double.  From  (45)  and  Table  XXV,  page  219,  the  thickness  must 
be  r76  inch,  the  distance  c  being  17.25  X  secant  45°  -  2  ft.  OtV  in. 

The  design  of  the  hip  vertical  U^  is  also  made  in  accordance 
with  (80)  of  the  Specifications.  It  will  be  assumed  that  the  section 
consists  of  one  8  by  f-inch  plate,  and  four  3£  by  3£  by  f-inch  angles, 
since  this  is  the  lightest  section  that  may  be  used  according  to  the 
Specifications,  the  8-inch  plate  being  chosen  as  it  gives  some  clearance 
between  the  inner  edges  of  the  legs  of  the  angles. 

The  total  stress  in  the  member  is  141  600  pounds,  and  the  unit- 
stress  is  16000  pounds  per  square  inch,  thus  requiring  a  net  area  of 
8.85  square  inches.  The  plate  gives  a 
net  area  of  2  .  20  square  inches,  and  the 
four  angles  give  a  net  area  of  6.88  square 
inches,  making  a  total  of  9.08  square 
inches,  one  rivet-hole  being  taken  out  of 
each  angle,  and  two  out  of  the  web,  at 
any  particular  section.  The  net  area  is 
somewhat  greater  than  that  required,  but 
must  be  used,  as  this  is  the  minimum  sec- 
tion allowed  by  the  Specifications.  Fig. 
176  shows  a  cross-section  of  this  member 
as  above  determined. 

This  member  will  be  connected  to  the  upper  chord  and  end-post 
by  means  of  a  pin  \vhich  is  6|  inches  in  diameter,  the  diameter  of  the 
pin  being  determined  later.  The  total  stress  is  141  600  pounds,  and 
this  will  be  taken  by  two  plates,  one  on  either  side  of  the  member. 
The  net  section  of  the  member  is  9.08  square  inches,  and  the  section 
through  the  pin  (26)  must  be  25  per  cent  in  excess  of  this,  making  a 
total  of  11.35  square  inches,  or  5.68  square  inches  for  each  plate. 
The  total  width  of  these  plates  will  be  taken  as  12  inches,  and  this 
(see  Fig.  177)  will  make  the  required  thickness: 
5.68  5.68 


Cross-Section,  of  Hip 
Vertical. 


Fig.  177  shows  the  details  of  these  pin-plates.  Since  the  above 
thickness  is  too  great  to  be  punched  in  one  single  piece,  the  above 
thickness  will  be  made  up  of  two  plates,  each  £  inch  thick.  The 
area  at  section  A-A  must  be  equal  to  that  of  the  body  of  the  bar.  It 


214 


BRIDGE  ENGINEERING 


is  12.00  X  ;>  =  6.00  square  inches  for  one  side,  or  12.00  square 
inches  for  both  sides.  As  this  is  greater  than  the  8 . 85  square  inches 
as  above  computed,  the  area  at  A-A  is  sufficient,  as  is  also  the  width 
of  the  plate,  which  was  assumed  as  12  inches. 

One  of  the  plates  will  be  riveted  directly  to  the  member,  and  the 
other  will  be  riveted  to  it  as  a  pin-plate.  The  section  back  of  the  pin 
(26)  must  be  equal  to  the  net  section  in  the  body  of  the  member.  The 
net  section  is  4.54  square  inches  for  one  side,  and  the  total  thickness 


Fig.  177.    Connection  of  Hip  Vertical  to  Upper  Chord  and  End-Post. 

of  the  pin-plates  is  1 . 125  inches,  making  the  distance  from  the  end 

4  54 

of  the  member  to  the  pin  - -'——  =  4|-  inches,  and  the  distance   to 
1 .125 

the  center  of  the  pin  4|  +  -^-  =  7|  inches. 

The  joint  between  the  plates  and  the  main  member  will  be  weak 
in  shear,  the  rivets  tending  to  shear  off  between  the  f-inch  angles  and 
the  plate,  and  also  between  the  two  plates  themselves.  As  each  side 
takes  one-half  of  the  above  stress,  the  number  of  rivets  required  to 
connect  the  plates  to  the  main  member  will  be : 
141  600  -  2 


7220 


=  10  shop  rivets, 


and  the  number  of  rivets  required  to  connect  the  inner  ^-inch  plate 
to  the  outer  one  which  is  connected  to  the  member  itself  will  be: 
141  600  -T-  4 


7  220 


=  5  shop  rivets. 


224 


BRIDGE  ENGINEERING 


215 


The  distance  from  the  center  of  the  pin  to  the  top  of  the  main 
part  must  be  greater  than  one-half  the  diameter  of  the  largest  I-bar 
head — that  is,  17^  -r-  2  =  say,  9  inches. 

At  the  lower  end,  this  member  is  connected  to  the  bottom  chord 
by  means  of  a  couple  of  clip  angles  and  four  or  five  rivets.  Only 
sufficient  rivets  are  required  to  prevent  the  sagging  of  the  bottom 
chord,  since  the  floor-beam  is  connected  to  the  hip  vertical  above  the 
lower  chord,  and  hence  no  stress  comes  on  the  joint  at  the  lower  end 
(see  Fig.  178). 

The  width  of  the  plate  has  been  assumed  as  8  inches.  This 
width  is  liable  to  be  changed  after  the  design  of  the  intermediate 


Fig.  178.    Connection  of  Hip  Vertical  to  Lower  Chord. 

posts  has  been  made,  since  it  will  be  economical  to  have  all  the  inter- 
mediate floor-beams  of  the  same  length;  and  therefore  the  width  of 
this  plate  will  be  changed  so  as  to  make  the  width  of  the  hip  vertical 
the  same  as  the  width  of  the  intermediate  posts. 

85.  The  Intermediate  Posts.  The  post  U2L2  must  be  designed 
to  stand  a  total  stress  of  163  GOO  pounds.  Where  possible,  it  is 
economical  to  make  the  intermediate  posts  out  of  channels,  as  this 
saves  a  large  amount  of  riveting.  As  seen  by  the  stress  sheet,  the 
length  of  these  posts  is  30 . 1  feet  center  to  center  of  end  pins.  It  is 

usually  required  that  —  must  not  be  more  than  100,  and  this  con- 
dition requires  that  the  least  radius  of  gyration  cannot  be  less  than 
30.1  X  12 


100 


3.62. 


210 


BRIDGE  ENGINEERING 


From  Carnegie  Handbook,  p.  101,  it  is  seen  that  a  12-inch  30- 
pound  channel  has  a  radius  of  gyration  of  4.28,  and  will  fulfil  the 
conditions.     The  area  of  two  of  these  channels  is  17 . 64  square  inches. 
The  unit  allowable  stress  (16)  is: 
30.1  x  12 


16  000  -  70  X 


4.28 


=  10  090  pounds  per  square  inch. 


1 63  600 
The  required  area  is  then  determined  to  be -7^7^  =  16.2  square 


V-5ShojD^-9  Shop 

he  Field 
1      go     ^      , 

,s  Shop      9  Shop 

LizField^ 

Fig.  170.    Cross-Section  of  Intermediate 
Post,  Showing  Diaphragm. 


inches;  and  as  this  coincides  very  closely  with  the  area  given,  these 

channels  are  efficient  and  will  be  used. 

Fig.   179  shows  the  cross-section  of  this  post.     The  radius  of 

gyration  which  was  used  above  was  the  radius  of  gyration  of  the  chan- 

nels about  an  axis  perpendicular 
to  their  web.  The  radius  of  gyra- 
tion of  the  entire  section  about 
an  axis  perpendicular  to  the 
web  will  be  the  same  as  that  of 
one  channel.  In  order  to  have 
the  sections  safe,  the  radius  of 
gyration  about  the  axis  B-B  must 
be  equal  to  or  greater  than  the 

other.       The    radillS    of    gvration 

8" 

about  the  axis  B-B  can  be  in- 
creased or  decreased  by  spacing  the  channels.  The  exact  distance 
which  will  make  the  two  rectangular  radii  of  gyration  equal  may 
be  determined  by  the  methods  of  "Strength  of  Materials,"  or  it 
may  be  found  in  columns  14  and  15  of  the  Carnegie  Handbook,  p. 
102.  For  any  particular  case  it  is  equal  to  the  value  given  in  column 
14,  plus  four  times  that  given  in  column  15.  For  the  channels  under 
consideration,  it  is  equal  to  7.07  +  4  X  0.704  =  9.  89  inches.  Any 
increase  in  this  distance  will  only  tend  to  increase  the  radius  of 
gyration  about  the  axis  B-B,  and  will  make  the  post  safer  about 
that  axis. 

Fig.  179  shows  a  diaphragm.  The  web  of  this  diaphragm  cannot 
be  less  than  f  inch,  and  the  size  of  the  angles  cannot  be  less  than  3^ 
by  3^  by  f  -inch,  as  this  is  the  least  allowed  by  the  Specifications.  The 
function  of  this  diaphragm  is  to  transfer  one-half  of  the  floor-beam 
reaction  to  the  outer  side  of  the  post.  The  rivets  which  connect  the 


226 


BRIDGE  ENGINEERING  217 

angles  to  the  diaphragm  web  are  shop  rivets,  and  (see  design  of  floor- 

1  O*7   P.f)f) 

beam)  must  be-  --  ^^7:  =  9  in  number.     The  rivets  which  connect 
2i  X  7  ooO 

the  diaphragm  angle  with  the  outer  channel  of  the  post  are  also  shop 

137  600 
rivets,  and  are  —  ^  —    oorT  =  ^  m   numDer>  5  on  each  side.     The 


same  rivets  which  connect  the  floor-beam  to  the  post  go  through 
the  diaphragm  angle  on  that  side  of  the  diaphragm  next  to  the  cen- 
ter of  the  bridge,  and  must  therefore  be  field  rivets  and  take  the 

137  600 

entire  floor-beam  reaction.      These  must  be^       —  -=  23  in  number, 

6  Olo 

12  on  each  side.  The  exact  distance,  back  to  back  of  the  channels  of 
the  post,  cannot  be  determined  until  after  the  top  chord  has  been  de- 
signed, since  the  post  must  slide  up  in  the  top  chord  and  also  leave 
room  on  each  side  for  the  diagonal  members  of  the  truss.  The 
width  is  determined  by  the  packing  of  the  members  at  joint  L2  (see 
Fig.  174),  and  is  found  to  be  9|  inches.  Since  this  is  less  than  that 
required  above,  the  post  must  be  examined  for  bending  about  an  axis 
parallel  to  the  web  of  the  channels. 

According  to  the  methods  of  "Mechanics"  and  "Strength  of 
Materials,"  with  the  help  of  the  Carnegie  Handbook,  p.  102,  the 
moment  of  inertia  about  this  axis  is  found  to  be  286.42,  and  the  ra- 
dius of  gyration  3  .96.  The  unit  allowable  compressive  stress  is  then 
computed  to  be  9  580  pounds  per  square  inch,  and  the  required  area 
1  no  p.r\f\ 
—  —  ---  =  17.10  square  inches,  which,  being  less  than  17.64,  shows 

the  section  to  be  safe. 

This  member  is  connected  to  the  top  chord  at  its  upper  end  by 
a  5-inch  pin.     The  total  stress  is  163  600  pounds,  and  the  total  bear- 

,  .     163  600 
ing  area  required  is  -^77^-  =  6.8  square  inches,  or  3.4  square  inches 


for  each  side  (19).     The  total  thickness  of  the  bearing  area  for  each 

side  is  ^—  =  0.68  inch.     The    thickness  of   the    web  of  a  12-inch 
o 

30-pound  channel  is  0.513  inch,  which  leaves  0.68  -  0.513  -  0.  167 
inch  as  the  thickness  of  the  pin-plate,  but  it  must  be  made  f  inch 
according  to  the  Specifications.  Fig.  180  shows  the  arrangement  of 
the  plates  and  the  rivets. 


218 


BRIDGE  ENGINEERING 


The  sum  total  of  the  pin-plates  and  the  channel  web  is  0.888 
inch,  and  therefore  on  one  side  the  stress  transferred  to  the  pin  by 

.     1  0  0.375  X  163  600 
means  of  the  pin-plate,  which  is  0.3/5  inch,  is  — -  X  — 

^  U . ooo 

=  34  600  pounds.    This  plate  will  tend  to  shear  off  the  rivets  between 

34  600 
it  and  the  channel  web,  and  therefore  =  5  shop  rivets  are 

,  /  ZiZ\} 

required. 

The  stress  that  is  shown  on  the  stress  sheet  is  the  stress  in  the 
post  above  the  floor-beam.     The  stress  in  that  part  below  the  floor- 


£T  

v                    I'jrij 

l'l 
rl  1    ' 

/ 
1 
\ 
\ 

|  0      0  J 

!©! 

i              ft 

-V-      J       liiF 

y 

1  1 

M 

J 



! 

01 

Li    \ 
)     l|y 

r 

1    ~--N 

1          !|!'l 

1 

1    l^i 

10 

01 

1    ^~-~-~ 

( 

1- 
t' 

b 

1 
1 

,     \               ;> 

,            x                             ii 

10 

|o 

10 

1 

0! 

o! 

1 

1 

I 

v'"                            ^ 

L 

J 

Fig.  180.    Arrangepient  of  Plates,  Rivets,  Pin,  etc.,  at  Connection  of  Intermediate  Post 
to  Top  Chord. 

beam  is  equal  to  the  vertical  component  of  the  diagonal  in  the  panel 
ahead  of  the  post  in  question.  In  this  case  it  is  the  vertical  com- 
ponent of  the  stress  in  V \L2,  and  is  equal  to  242  000  pounds,  and  this 

„  242  000 
requires  a  total  bearing  area  ot  -7^77^-  =  10.1  square  inches,  and 

a  total  thickness  of 


24000 
1.01  inches  on  each  side,  the  pin  being 


2X5 

5  inches  in  diameter.  From  this  total  thickness  must  be  subtracted 
the  thickness  of  the  web  of  the  channel,  and  this  leaves  1.01  —  0.513 
=  0.497  inch  as  the  total  thickness  of  the  pin-plates  required.  This 
shows  that  we  must  use  one  ^-inch  plate.  The  total  thickness  of  the 
bear  ing  area  is  now  0.51  3  +  0.50  =  1.013  inches. 


Each  plate  takes  a  total  stress  of 


1  .013 


949  nnn 
X  =  59  700 


BRIDGE  ENGINEERING 


219 


pounds;  and  the  joint  being  weak  in  shear,  the  number  of  rivets 

59  700 
required  will  be   — — =  9  rivets  in  single  shear.     The  detail  will  be 

/    _  — V ) 

similar  to  that  in  Fig.  180. 

The  distance,  back  to  back  of  the  channels  in  this  post,  will 
probably  not  be  greater  than  12  inches,  and  this  will  make  the  dis- 
tance between  rivet  lines  about  9  inches.  According  to  (44),  the  end 
tie-plates  must  be  at  least  9  inches  long  and  of  course  12  inches  wide. 

g 

The  thickness  cannot  be  less  than  — •  =  0 . 18  inch,  but  they  will  be 

50 

made  f  inch  (36).     Between  the  tie-plates  the  channels  will  be  con- 
nected by  means  of  lattices.     The  Specifications  (45)  require  that 

they  should  not  be  less  than  2\  inches  in  width  and  (1 .414  X  9)  —  = 

0.318  (say  f)  inch  in  thickness.     Table  XXV  gives  the  thickness  of 
lacing  bars  for  any  distance  between  rivets. 

TABLE  XXV 
Thickness  of  Lacing  Bars 


xxv<> 


LJL 


SINGLE  LACING 

('=*>'  *=«>•) 

DOUBLE  LACING  (*=^:   0  =  45°) 

t 

« 

t 

c 

i  in. 

Oft.  10    in. 

i  in. 

1  ft.    3    in. 

A  in- 

1  ft.    0£  in. 

A  in- 

1  ft.    6|  in. 

t  in.     - 

1  ft,    3    in. 

1  in. 

1  ft.  lOJt  in. 

I7«  in. 

1  ft.     Si  in. 

T7s  in- 

2ft.    2i-in. 

Jt  in. 

1  ft,    8    in. 

i  in. 

2  ft.    6    in. 

T«  in- 

1  ft.  10*  in. 

T»  in. 

2ft.    9|in. 

f   in- 

2ft.     1    in. 

t  in. 

3ft.     liirf. 

A  width  of  2}  inches  is  chosen  above,  since  according  to  Carnegie 
Handbook,  p.  183,  a  |-inch  rivet  is  the  largest  which  can  be  used  in 
the  channel  flange. 

The  post  U3L3  must  be  designed  for  a  total  stress  of  87000 
pounds.  It  will  be  assumed  that  two  10-inch  20-pound  channels 


220  BRIDGE  ENGINEERING 

with  a  radius  of  gyration  3 .66  and  an  area  of  5 .80  square  inches  each 
will  be  sufficient.  The  length,  as  before,  is  30.1  feet,  and  the  unit- 
stress  is: 

P  =  16  000  -  70  X  -  —  =  9  080  pounds. 

3.66 

The   required    area    is  —  =9.60   square   inches.      Since   the 

y  080 

total  area  of  the  two  channels  is  11 .76  square  inches,  and  the  required 
area  is  9.6  square  inches,  it  is  seen  that  they  do  not  coincide  very 
closely.  These  channels,  however,  will  be  used,  since  the  thickness 
of  the  web  is  the  thinnest  allowed  by  the  Specifications,  and  the 
width  of  the  channels  is  the  smallest  that  can  be  used  and  still  give 
sufficient  room  to  make  the  connections  with  the  end  connection 
angles  of  the  floor-beams. 

The  lower  end  of  this  post  also  has  a  diaphragm  which  must 
transfer  half  of  the  stress  to  the  outer  channel  of  the  post.    The  sides 

of  the  diaphragm  are  the  same 
as  in  the  posts  previously  de- 
signed ;  and  the  number  of  rivets 

^    ~)/5      °P^~      3P  |   ^  p..^  required  is  computed  in  a  simi- 

\     j"?    ")  -v       lar  manner  and  found  to  be  as 
^sSho     9^(5    I   I' rie     •  indicated    in    Fig.    181,   which 

shows  the  cross-section  of  this 
post. 

At  the  upper  end  the  bear- 
Fig.  181.    Cross-Section  of  Intermediate          .  Li, 

Post.  ing  area  required  on  one  chan- 

cy i  nn 

nel  is- —  =  1.814  square  inches,  and  the  thickness  required 

*-•  /\  ^4  UUU 

1  814 

is  — =  0.363  inch,  a  5-inch  pin  being  used.     As  the  web  of  the 

5 

channel  is  0.382  inch  thick,  it  will  give  sufficient  bearing  area 
without  pin-plates. 

At  the  lower  end,  the  vertical  component  of  £7,Z,3  is  157  500 
pounds.     The  bearing  area  required  on  each  side  of  the  post  is 

157  500  3  28 

3.28  square  inches,  and  the  thickness  is  —        =  0.66 


£    s\    ^i~L  UUvJ 

inch.  The  thickness  of  the  channel  web  being  0 . 382  inch  leaves  0 . 660 
—  0.382  =  0.278  inch  as  the  required  thickness  of  the  pin-plate; 


BRIDGE  ENGINEERING 


221 


but  f  inch  must  be  used,  making  a  total  thickness  of  0.382  +  0.375 

=  0.757  inch.     The    plate    will    carry    ~^.5  X  ~—  =  39  000 

39000 
pounds,  and  this  requires =  6  shop  rivets  in  single  shear. 

The  distance,  back  to  back  of  channels,  will  be  the  same  as  in 


T 

T  r 

/s 

/  \ 

/      \ 

/      \ 

/            , 

(            \ 

/               \ 

\            \ 

/               / 

\          \ 

/               / 

\ 
\ 

s 

/ 

\ 

x 

/ 

/ 

\ 

\ 

-cT1 

'%' 

.   / 

i  "T 

s*. 

i^ 

7'  •? 

/        | 

1  Jxs 

Lfe 

|i 

i^  1 

P  * 

Is 

4 

1°  ( 

•V  04, 

) 

C 

—  ^ 

<^ 

] 

Fig.  182.    End  and  Side  Elevations  Showing  Detail  of  Construction  at  Lower  End  of 
Intermediate  Post. 

C/2L2,  and  therefore  the  tie-plates  and  lacing  bars  will  be  the  same. 
Fig.  182  gives  a  detail  of  the  lower  end  of  U3Ly 

86.  The  Top  Chord.  The  top  chords  of  small  railway  bridges 
may  be  made  of  two  channels  laced  on  their  top  and  bottom  sides. 
This  is  not  very  good  practice,  since  it  leaves  the  tops  of  the  channels 
open  and  lets  in  the  rain  and  snow,  wjiich  tends  to  deteriorate  the 
joints.  It  is  better  to  add  a  small  cover-plate,  even  if  this  does  give 


222 


BRIDGE  ENGINEERING 


an  excessive  section.  In  case  of  stress  such 
as  is  demanded,  the  chords  may  consist  of 
two  channels  and  a  cover-plate.  In  this 
case  it  is  necessary  to  place  small  pieces 
called  flats  upon  the  lower  flanges  of  the 
channel,  in  order  to  lower  the  center  of 
gravity  of  the  section  and  to  bring  it  near 
the  center  of  the  web.  This  section  makes 
a  very  economical  section  in  that  it  saves 
much  riveting.  On  account  of  channels 
being  made  only  up  to  15  inches  in  depth, 
'the  use  of  this  section  is  quite  limited  owing 
to  the  fact  that  it  is  not  deep  enough  to 
allow  the  I-bar  heads  sufficient  clearance, 
for  the  I-bar  heads  in  bridges  of  even  ordi- 
nary span  will  exceed  this  amount. 

The  most  common  section  is  that  which 
consists  of  two  side  plates,  four  angles,  and 
one  cover-plate.  Sometimes  this  section 
has  flats  placed  upon  the  lower  angle  in 
order  to  lower  the  center  of  gravity,  as  ex- 
plained above.  According  to  (33),  the  sec- 
tion should  be  as  symmetrical  as  possible, 
and  the  center  of  gravity  should  lie  as  near 
the  center  of  the  web  as  is  consistent  with 
economy. 

In  case  the  stress  is  great  enough  to 
demand  a  heavier  section  than  that  above 
described,  additional  plates  are  added  upon 
the  sides  of  the  original  plates,  and  heavier 
and  larger  cover-plates  and  angles  are  used. 
Fig.  183  shows  different  types  of  chord  sec- 
tions. 

Ir  addition  to  the  cover-plate  being 
designed  to  withstand  the  total  stress,  close 
attention  must  be  paid  to  (42).  This  clause 
has  been  inserted  on  account  of  practical 
considerations,  since  it  has  been  found  out 


BRIDGE  ENGINEERING  223 

that  if  plates  are  made  much  thinner  than  the  proportions  here 
required,  they  will  crumple  up  and  fail  long  before  the  allowable 
unit  of  stress  as  computed  from  the  formula  has  been  .reached.  In 
some  cases  —  especially  where  the  stress  is  light  —  the  proportions  laid 
down  in  (42)  and  (36)  will  govern  the  design  of  the  section,  instead  of 
the  required  net  area  as  determined  by  the  formula  for  the  allowable 
unit  compressive  stress. 

The  design  of  the  first  section  of  the  top  chord  will  now  be  made. 
Here,  as  in  the  case  of  the  first  sections  of  the  lower  chord,  the 
diameter  of  the  head  of  the  greatest  I-bar  determines  the  width  of  the 
plates  in  the  section  The  head  of  the  7-inch  I-bar  wThich  constitutes 
the  member  UtL2  is  17^  inches,  and,  allowing  a  clearance  of  \  inch 
on  either  side  of  the  head,  the  total  depth  inside  the  chord  should  be 
18J  inches.  As  in  the  case  of  the  lower  chord,  plates  18  inches  wide 
may  be  used. 

The  size  of  the  angles  to  be  chosen  is  a  matter  of  judgment. 
Usually  any  size  should  be  chosen  at  first,  and  the  preliminary  design 
will  indicate  at  once  what  size  should  have  been  taken.  For  this  case, 
3a  by  3i  by  f-inch  will  be  assumed  at  first. 

For  sections  of  this  character,  the  radius  of  gyration  is  approxi- 
mately equal  to  OAh,  in  which  h  is  the  height,  or  rather  the  width, 
of  the  side  plate.  The  approximate  radius  of  gyration  is  r  =  0.4  X 
18  =  7.  2  inches,  and  the  length  is  equal  to  one  panel  length,  or  21 
feet.  The  allowable  unit  of  stress  (16)  is: 

P  =  16  000  -  70  X    21  X212   =  13  550  pounds. 

449  500 
The  required  area  is-r^^vr-  =  33.2  square  inches.     The  correct 


proportion  for  sections  of  this  character  is  that  0  .  4  of  the  total  area 
should  be  taken  up  by  the  web.  The  area  of  the  web  would  then  be 
0.4  X  33.2  =  13.28  square  inches,  and  the  thickness  would  be 

1  *3  28 

0  =  0.37  inch.    According  to  this,  a  f-inch  plate  should  be  used, 
2  X  18  14  ^ 

but    (42)   requires  that  it   shall  be.-^r-  =  0.483  inch  or    thicker. 

Therefore  an  18  by  i-inch  plate  must  be  used  for  the  web. 

The  correct  proportion  for  sections  of  this  character  is  that  the 
width  between  plates  should  be  about  f  the  width  of  the  side  plates. 


224 


BRIDGE  ENGINEERING 


This  will  give  the  required  width  between  plates  equal  to  £  X  18  = 
15.75   inches.     The  cover-plate  (42)  must  not  be  thinner   than  — 

the  distance  between  the  connecting  rivet  lines.     The  rivet  lines  are, 
in  this  case,  15.75  +  2  X  2  =  19.75  inches  apart,  and  therefore  the 

19  75 
thickness  of  the  cover-plate  cannot  be  less  than 


40 


0.494  inch. 


The  cover-plate  will  therefore  be  taken  as  \  inch  thick.     The  width 

of  the  cover-plate  (see  Fig.  184) 

|t  i9j?" d  must  be  about  15.75  +  2  X  3£ 

+  \  =  231  inches  (say  23  inches). 
The  cover-plate  will  be  taken  23 
by  i-inch. 

The  center  line  of  pins  will 
be  taken  at  the  center  line  of  the 
w7eb,  and  the  center  of  gravity  of 
the  section  will  be  assumed  as  ^ 
inch  above  this.  In  order  that 
the  center  of  gravity  may  be  near 
that  assumed,  the  moment  of  the 
cover-plate  about  the  assumed 
center  of  gravity  axis  should  be 
about  equal  to  the  moment  of  the 
flats  about  the  same  axis.  The 

moment  of  the  cover-plate  about  the  assumed  axis  is: 


gPlS.  18"xgPls 

Neutral  AMS^ 

Center  Line  of  Pins? 


qpprox. 


Fig.  184.     Section  of  Top  Chord. 


23  X 


23    V   Q 
(9.0  -  0.5  +  0.25  +  0.25)  =          *       ; 


and  the  moment  of  the  flats  about  the  same  axis  is: 
A  (9.0  +  0.5  +  0.25  +  0.5)  =  10.25,4, 

in  which  A  is  the  area  in  square  inches  of  both  of  the  flats.     Equating 
these  two  expressions,  and  solving  for  A,  there  results: 
23  X  9 


A  =   .- 


10.1  square  inches. 


2  X  10.25 

Assuming  the  flats  to  be  4  inches  wide,  the  thickness  on  each  side 
will  be  1 .25  inches.     As  this  is  too  thick  to  punch,  the  flats  on  each 
side  will  be  composed  of  two  4  by  f-inch  plates. 
The  total  area  is : 


234 


BRIDGE  ENGINEERING  225 


One  cover-plate  =  2.3  X  i  =  11.5  sq.  in. 

Two  web  plates  =  2  X  18  X  i    =18.0     "    " 
Two  flats  4  X  1J  =  10.0     "    " 


Total     39 . 5     sq.  in. 

But  the  required  area  is  32.2  square  inches,  which  is  considerably 
less  than  the  area  above  given,  and  which  does  not  include  the  angles 
and  hence  we  can  use  the  smallest  size  angles,  which  are  those  pre- 
viously assumed.  The  area  of  each  of  these  angles  is  2.48  square 
inches,  thus  making  the  total  area  of  the  section  39 . 5  +  4  X  2 . 48  = 
49.42  square  inches.  This  is  considerably  in  excess  of  the  area  as 
required  according  to  the  formula  for  compression;  but  it  is  the  least 
allowed  by  the  Specifications.  Note  that  this  is  the  case  where 
(42),  instead  of  the  formula  for  compressive  stress,  is  the  ruling  factor 
in  the  determination  of  the  section. 

The  center  of  gravity  of  the  approximate  section  must  now  be 
determined,  the  moment  of  inertia  and  the  radius  of  gyration  about 
the  neutral  axis  must  be  computed,  and  the  required  area  must  be 
determined  by  using  this  radius  of  gyration  as  computed.  If  the 
required  area  as  determined  with  the  actual  radius  of  gyration  is  less 
than  the  approximate  area,  then  the  thickness  of  the  angles  or  the 
plates  must  be  increased  and  the  section  then  examined  for  its  radius 
of  gyration  and  required  area.  If  the  area  is  sufficient,  the  section 
is  used;  if  not,  another  recomputation  is  in  order. 

In  the  determination  of  the  center  of  gravity  of  the  section,  the 
moment  is  taken  about  the  top  of  {lie  cover-plate.  The  moments  are 
computed  as  follows: 

Cover- plate  (23  X  *)  X  \ 2 . 88 

Webs  2  (18  X  i)  X  (9  +  |) 175.60 

Top  angles  2  (2.48)  X  (1.01  +  i) 7.50 

Lower  angles  2  (2.48)  X  (J  +  i  +  18  H-  \ -  -  1.01) 89.30 

Flats" 2  (4  X  H)  X  19| 196.25 


Total  ......  471.53 

The  center  of  gravity  is  newfound  to  be  7^-^.  —  -   =9.55 

4  X  2.48 


inches  from  the  top  of  the  cover-plate.  The  distance  from  the  top  of 
the  cover-plate  to  the  middle  line  of  the  web  is9+j  +  ^  =  9.75 
inches,  and  this  leaves  a  distance  of  9.75*  —  9.55  =  0.2  inch  from 
the  center  line  of  the  web  to  the  neutral  axis.  This  distance  is  gen- 


226  BRIDGE  ENGINEERING 

erally  represented  by  the  letter  e,  and  it  is  known  as  the  eccentricity  of 
the  section. 

The  moment  of  inertia  about  this  axis  must  now  be  computed. 
The  relation  used  is  that  the  moment  of  inertia  about  any  axis  is 
equal  to  the  moment  of  inertia  about  some  other  axis,  plus  the  product 
of  the  square  of  the  distance  between  the  two  axes  by  the  area  of  the 
section  whose  moment  of  inertia  is  desired.  The  moments  of  inertia 
of  the  various  parts  of  the  section  (see  "Steel  Construction,"  Part 
IV,  pp.  292  and  293)  are  computed  and  are  as  follows: 

Cover-plates 955 . 26 

Webs 486 . 72 

Top  angles 325 . 74 

Lower  angles '.      359 . 74 

Flats...  ..-1017.37 


Total.  .      ..  3  184.83 


The  radius  of  gyration  is  equal  to  the  square  root  of  the  quotient 
obtained  by  dividing  the  moment  of  inertia  by  the  area.     It  is 


r  =  J3  184'83    =  8.04. 
Af     49.42 

Using  this  value  of  the  radius  of  gyration  in  the  formula  for  the  com- 
pressive  stress,  there  is  obtained  13  800  pounds  as  the  unit  allowable 

,  449  500 

stress  in  compression,  and  this  requires  an  area  or  —  =32.5 

13  800 

square  inches.  Since  this  is  considerably  less  than  the  actual  area  of 
the  section,  the  section  will  not  be  changed  but  will  be  taken  as  first 
assumed. 

In  order  that  the  section  should  be  safe  about  both  axes,  the 
moment  of  inertia  about  the  axis  perpendicular  to  the  cover-plate 
should  be  equal  to  or  greater  than  that  as  above  computed.  By  com- 
puting the  moment  of  inertia  about  the  axis  perpendicular  to  the 
cover-plate,  it  is  found  to  be  3  256 .3,  which  gives  a  radius  of  gyration 
of  8 . 1 1 ;  and  since  both  of  these  are  greater  than  those  first  computed, 
it  is  seen  that  the  section  is  safer  about  the  axis  perpendicular  to  the 
cover-plate  than  it  is  about  an  axis  perpendicular  to  the  web  plates. 

There  are  small  stresses  in  this  member  due  to  its  own  weight 
and  to  the  fact  that  the  pins  are  not  placed  directly  upon  the  neutral 
axis  (see  "Strength  of  Materials,"  p.  82).  These  stresses  are  seldom 
more  than  1  000  pounds  per  square  inch  in  the  extreme  fibre;  and 


236 


BRIDGE  ENGINEERING  227 

since  the  section  has  such  an  excess  of  area,  they  will  not  be  computed, 
as  it  is  evident  that  there  is  sufficient  strength  in  the  member  to  with- 
stand them. 

The  section  just  designed  is  that  for  the  top  chord  having  the 
greatest  stress;  and  since  this  is  the  minimum  section  allowed  by 
the  Specifications,  it  must  be  used  in  all  the  sections  of  the  top  chord. 

The  section  as  finally  designed  is: 

One  cover  plate,  23  by  i  inch; 
Two  webs,  18  by  \  inch; 
Four  angles,  3£  by  3^  by  f  -inch 
Four  flats,  4  by  f-inch. 

A  pin  6j  inches  in  diameter  wrill  be  used  at  the  point  Ur  The 
stress  in  the  member  UJJ2  is  378  200  pounds,  and  the  bearing  area 

378  ^00 
required  is  —  -  -  =  15.  75  square  inches,  or  7.875  for  each  side. 

7  875 
This  makes  a  total  required  thickness  of    '         =  1  .  265  inches  for  one 

side.  Since  the  thickness  of  the  web  plate  is  ^  inch,  it  will  be  necessary 
to  provide  pin-plates  whose  total  thickness  must  be  1.265  —  0.5  = 
0  .  765  inch.  Two  f  -inch  plates  will  give  a  thickness  of  0  .  75  inch  ;  and 
since  this  is  less  than  the  required  thickness  by  an  amount  not  over 
2\  per  cent,  they  may  be  used.  The  total  thickness  of  the  bearing 
area  is  now  1  .  265  inches.  The  stress  transferred  to  the  two  f  -inch 
plates  is: 

s  =          JL  X  189  100  =  113  500  pounds. 


The  rivets  required  to  keep  the  outer  plate  from  shearing  off  the 

113  500 
other  are  -  -  —-•     =8  shop  rivets,  and  the  rivets  required  to  keep  both 

^  X  /  2ZO 

of  the  |  -inch  plates  from  shearing  off  the  web  of  the  chord  section  are 

I  1  O    !XAf) 

~~7~99ff~  =  ^  shop  rivets  in  single  shear.     The  bearing  of  a  f-inch 

shop  rivet  on  a  |-inch  plate  is  10  500  pounds,  and  therefore  the  num- 
ber of  rivets  required  to  keep  these  pin-plates  from  tearing  the  rivets 

113  500 

out  of  the  *>-inch  web  plates  is  —  —  —  =11  shop  rivets  in  bearing. 
10  500 

Fig.  185  shows  the  detail  of  this  end  of  the  top  chord  section.     The  pin- 
plates  should  extend  well  back  on  the  member,  and  at  least  one  pin- 


237 


228 


BRIDGE  ENGINEERING 


plate  should  go  over  the  angle,  and  enough  rivets,  as  computed  above, 
should  go  through  the  angles  and  this  pin-plate.  Experiments  on  full- 
sized  bridge  members  go  to  show  that  unless  the  pin-plates  cover  the 
angles  and  extend  well  down  on  the  member,  the  member  will  fail 

O 

before  the  unit-stress  reaches  that  value  computed  by  the  formula 
for  compression. 

Since  the  ends  of  the  chord  are  milled  at  the  splices,  and  therefore 
butt  up  against  each  other  and  allow  the  stress  to  be  transmitted 


,0000 


0 

O  O 

•gPlate 

0..0 

2        8  Plate 

p 

O 

0   0 

0 

0   0 

\ 

0  0 

O  O   O  I 

Fig. 


Detail  of  Top  Chord  Section  at  Point  Ur 


directly,  only  sufficient  rivets  need  be  placed  in  the  splice  to  keep  the 
top  chord  sections  in  line  (55). 

At  the  point  U2,  it  is  not  necessary  to  put  in  a  pin-plate  to  take 
the  stress  in  the  upper  chord;  but  it  is  only  necessary  to  provide  a 
pin-plate  to  take  up  the  difference  in  stress  between  the  two  chord 
sections.  This  difference  in  stress  is  equal  to  the  horizontal  com- 
ponent of  the  maximum  stress  in  the  member  U2L3.  This  is  110  000 
pounds,  and  the  area  required  on  each  side  for  bearing  is  2.3  square 
inches;  and  as  a  5-inch  pin  is  used  here,  the  thickness  of  the  bearing 

inch.     As  this   thickness  is  less  than  the  thick- 


2  3 

area  is  -—  =  0.46 
5 


ness  of  the  web  plate,  no  pin-plates  will  be  required. 

At  the  point  U3,  a  bearing  area  will  be  required  to  withstand  the 
horizontal  component  of  the  member  U3L4.     This  is  56  300,  and  the 


BRIDGE  ENGINEERING 


229 


bearing  area  required  on  each  side  is 


56300 
24  000  X  2 
1.18 


=  1.18  inches.  The 


required  thickness  of  the  bearing  area  is   -J—  =  0.24  inch,  as  a  5- 

5 

inch  pin  is  used  here  also.     As  this  thickness  is  less  than  the  thickness 
of  the  web  plate,  no  pin-plate  will  be  required. 

The  under  parts  of  these  members  must  be  stiffened  by  tie  or 
batten  plates,  and  these  plates  (44)  must  be  equal  in  length  to  the 
distance  between  rivet  lines.  This  is  19n  inches.  They  will  be  made 
20  inches  long  and  23  inches  wide.  The  thickness  of  these  plates  (44) 

must  be  —  '—  =  0.39  inch  (say  TV  inch).     The  size  of  the  tie-plates 
50 

will  then  be  20  in.  by  W  in.  by  1  ft.  11  in. 

Since  the  distance  between  the  rivet  lines  is  greater  than  15 
inches,  double  latticing  must  be  used  (47);  and  according  to  Table 
XXV  the  lacing  must  be  \  inch 
thick;  also,  according  to  (45),  it 
must  be  1\  inches  wide,  as  the 
rivets  used  are  \  inch  in  diam- 
eter. The  lattices  will  then  be 
2-fc  by  4-in. 

87.  The  End=Post.  Since  the 
minimum  section  as  chosen  for 
the  top  chord  is  about  50  per 
cent  in  excess  of  that  required  by 
the  compression  formula,  it  will 
be  assumed  to  be  sufficient  for 


pig 


Calculation  of  End.Pos, 


the  section  of  the  end-post,  and 

it  will  now  be  investigated  to  see  if  it  is  safe. 

In  addition  to  the  stress  due  to  direct  compression,  the  end-post 
is  stressed  by  its  own  weight,  by  eccentric  loading  due  to  the  pin  being 
in  the  center  of  the  web  instead  of  at  the  center  of  gravity  of  the 
section,  and  to  a  bending  moment  at  the  place  wThere  the  portal  brace 
joins  it.  This  is  due  to  the  bending  action  of  the  wind  on  the  top 
chord.  These  different  stresses  will  now  be  computed;  and  since  the 
post  is  in  all  cases  stressed  by  a  combination  of  bending  and  compres-, 
sive  stresses,  this  fact  should  be  considered  in  the  design.  In  deter- 
mining the  stress  in  the  end-post  due  to  its  own  weight,  the  entire 


239 


230  BRIDGE  ENGINEERING 

weight  must  not  be  used  in  computing  the  bending  action,  but  only 
that  component  of  it  which  is  perpendicular  to  the  end-post.  The 
length  of  the  end-post  is  readily  computed,  and  is  as  shown  in  Fig. 
186.  The  general  formula  for  accurately  computing  stresses  due  to 
bending  when  the  member  is  also  subjected  to  compression,  is: 

My, 

~/T^T 

WE 
in  which, 

S  =  Stress  in  pounds  per  square  inch  in  the  extreme  upper  fibre  of  the 

beam; 

M  =  Exterior  moment  causing  the  stress,  and  is  considered  positive  if  it 
bends  the  beam  downward,  and  negative  if  it  bends  the  beam  up- 
ward; 

?/,=  Distance  from  the  neutral  axis  to  the  extreme  upper  fibre; 

/  =  Moment  of  inertia  of  the  section; 

P  =  Direct  compressive  stress,  in  pounds; 
I  =  Total  length,  in  inches; 

E  =  Modulus  of  elasticity  of  steel,  which  is  usually  taken  as  28  000  000 
pounds  per  square  inch. 

In  this  case  the  force  causing  the  bending  is  that  component  of 
the  weight  perpendicular  to  the  end-post.  This  is  Wl  sinf'>,  in  which 
W  is  the  weight  of  the  steel  in  the  end-post;  and  this  is  computed  and 
is  as  follows: 

Cover-plate 1  435  Ibs. 

Web  plates '. 2245" 

Angles 1250" 

Flats...  ..1245" 


6  175  Ibs. 
Add  25  per  cent  for  details 1  544  " 


Total.  ...  7  719  Ibs. 

Substituting  in  the  above  formula  the  various  values,  there  results: 
X  7  719  X  36.7  X  0.572  X  12  X  9.55 


S  =   -- 


,  1C.        410500  X  (36.7  X  12)2 
o  loo  — 


10  X  28  000  000 
=  800  pounds  per  square  inch  compression   in  the  tipper 
fibre  due  to  bending. 

In  the  above  equation,  the  stress  in  the  member  is  410  500  pounds; 
the  distance  yl  is  the  distance  from  the  neutral  axis  to  the  top  of  the 
cover-plate,  and  the  coefficient  of  elasticity  of  steel  is  taken  as 
28  000  000. 


240 


BRIDGE  ENGINEERING 


231 


In  computing  the  stress  due  to  the  eccentric  loading,  the  moment 
is  equal  to  the  product  of  the  total  stress  in  the  member  by  the  dis- 
tance~from  the  neutral  axis  to  the  center  of  gravity  axis  causing  a 
negative  moment.  Substituting  in  the  above  formula  for  combined 
stresses,  there  results: 

-  410500  X  0.2  X  9.55 


S  =   - 


3  185  - 


410500  X  (36.7  X  12)2 


4  £70 


10  X  28  000  000 
=  270  pounds  per  square  inch  tension  in  the  upper  fibre. 

In  order  to  find  the  compression  in  the  lower  fibre,  it  is  only  necessary 
to  notice  that  the  stresses  are  proportional  to  the  distances  from  the 
neutral  axis.  Accordingly  (see  Fig.  187), 
the  stress  in  the  lower  fibre  due  to  the 
weight  is  895  pounds  tension,  and  the 
stress  in  the  lower  fibre  due  to  the  eccen- 
tric loading  is  302  pounds  compression. 

Before  computing  the  stress  due  to  the 
bending  moment  caused  by  the  wind  on 
the  upper  chord,  it  is  necessary  to  in- 
vestigate the  post  to  see  if  it  is  fixed  or 
hinged  at  its  lower  end.  This  is  very 
important,  since,  if  the  post  is  found  to 
be  hinged,  the  bending  moment  will  be 
one-half  of  that  which  will  occur  when 
the  post  is  not  hinged. 

An  end-post  is  considered  hinged  when  the  product  of  one-half 
of  the  total  stress  times  the  distance  between  the  web  plates  is  greater 
than  the  product  of  the  wind  load  acting  at  the  hip,  or  joint  Uv  times 


Fig.  187.    Calculation  of  Stress 
in  Chord. 


the  length  of  the  end -post.     In  this  case  the  first  value  is 


410  500 


X 


15  =  3075000;  and  the  product  of  the  latter  (see  Article  29)  is 
12  600  X  36.7  X  12  =  5  550  000.  Since  the  latter  is  greater  than 
the  former,  the  post  is  hinged,  and  the  bending  moment  at  the  foot 
of  the  portal  strut,  which  joins  the  end-post  28.2  feet  from  the  end,  is 
6300  X  28.2  X  12  -  2130000  pound-inches.  The  stress  in  the 
extreme  fibre  due  to  this  bending  moment  is: 
2  130000  x  11.5 


3256.3  - 


410500  X  (36.7  X  12)a 
10  X  28  000  000 


241 


232  BRIDGE  ENGINEERING 

=  8  250  pounds  per  square  inch  tension  or  compression. 
In  computing  this  stress  due  to  the  wind  moment,  care  must  be  taken 
to  take  yt  equal  to  one-half  the  width  of  the  cover-plate,  and  to  take 
'the  moment  of  inertia  as  that  about  the  axis  perpendicular  to  the 
cover-plate. 

In  computing  the  total  stress  on  the  extreme  fibre,  it  must  be 
noted  that  the  stresses  due  to  weight  and  eccentric  loading  do  not 
stress  the  same  extreme  fibres  as  the  stress  due  to  wind,  the  former 
stressing  the  extreme  fibres  on  the  top  and  bottom  of  the  post,  while 
the  latter  stresses  those  on  the  inner  and  outer  sides.  The  total 

direct  unit-stress  is  —  —  8310  pounds  per  square  inch;   and 

this,  added  to  the  8  250  pounds  per  square  inch  due  to  the  wind, 
gives  a  total  of  16  560  pounds  per  square  inch  on  the  extreme 
fibre  only. 

oc   7  v  1 9 

The  allowable  unit-stress  is  16  000  -  70  X-  -  =  12  200 

8. 11 

pounds  per  square  inch  when  wind  is  not  taken  into  account,  and 
(23)  is  \\  X  12  200  =  15  250  pounds  per  square  inch  when  the  wind 
is  taken  into  account.  The  difference  between  this  and  the  actual 
stress  is  16  560  —  15  250  =  1  310  pounds  per  square  inch,  which 
shows  that  the  section  is  not  strong  enough.  The  section  can  be  in- 
creased by  widening  the  cover-plate  or  by  making  the  plates  thicker ; 
but  as  this  excess  is  due  to  wind  only,  the  section  being  amply  suffi- 
cient under  the  other  stresses,  and  is  fixed  to  some  extent  by  the 
floor-beam  connection,  no  change  will  be  made. 

The  pin  at  each  end  of  the  end-post  will  be  the  same — namely, 
6]  inches  in  diameter — and  therefore  the  pin-plates  will  be  the  same 
at  each  end.  The  total  stress  in  the  post  is  410  500  pounds,  which 

„  410  500 

makes   a  required  bearing  area  of  1777.^  =  17.2  square  inches  for 

^.4  UUU 

both  sides,  or  8.6  square  inches  for  one  side,  and  the  total  required 

Q      £* 

thickness  of  — '—  =  1.375  square   inches   for  one  side.     Since    the 

thickness  of  the  web  plates  is  \  inch,  this  leaves  a  remainder 
of  1.375  —  0.5  =  0.875  inch  for  the  thickness  of  the  pin-plates. 
One  plate  f  inch  thick  and  one  plate  \  inch  thick  will  be  used. 

The  proportion  of  the  total  stress  which  is  taken  by  the  f-inch 


242 


BRIDGE  ENGINEERING 


233 


0.375       410500 


56  000  pounds;  and  that  taken  by  the 


|-inch  plate  is  -^— -  X  205250  = '74  600  pounds.  The  number  of 
rivets  required  to  transfer  the  stress  from  the  f-inch  plate  to  the  |-inch 
plate  is  =  8  shop  rivets  in  single  shear;  and  the  number  of 

rivets  required  to  transfer  the  stress  from  both  pin-plates  to  the  web  is 

56  000  +  74  600  •    *    •      •  i    • 

—  =18  shop  rivets  in  single  shear.     As  in  the  case  of 


the  top  chord,  one  pin-plate  should  extend  over  the  angle,  and  the 

number  of  rivets  required  in  that  pin-plate  should  go  through  the  pin- 

plate  and   the  angles   (see   Fig. 

188).     The  |-in.  hinge  plate  is 

used  for  erection  purposes,  and  is 

not  considered  as  a  pin-plate.    It 

is  omitted  at  L0. 

Since  this  section  is  the  same 
as  that  of  the  top  chord,  the  tie- 
plates  and  the  lattice  bars  must 
be  the  same  size. 

88.  The  Pins.  The  design  of 
the  pins  requires  a  simple  but 
quite  lengthy  computation.  Sim- 
ple Pratt  railroad  trusses  for 
single-track  bridges  usually  have 
the  same  arrangement  of  tension 

and  compression  members;  that  is,  the  same  tension  members  occupy 
relatively  the  same  positions  with  respect  to  the  compression  mem- 
bers. Also,while  theoretically  a  different  sized  pin  will  be  required  at 
every  joint,  it  is  not  customary  to  make  them  so.  In  practice  the 
pins  at  the  joints  U^  and  JL0  are  made  of  the  same  diameter,  and 
those  at  the  remainder  of  the  joints  are  also  made  in  diameter  equal 
to  each  other  but  different  from  those  at  Ul  and  Z/0,  the  pins  at  U\ 
and  L0  usually  being  larger  in  diameter.  On  account  of  the  above 
conditions  and  facts,  it  is  unnecessary  to  design  the  pins  in  spans 
under  200  feet,  since  usually  they  are  the  same  for  any  given  span 
and  loading.  Table  XXVI  gives  the  diameters  of  pins  for  spans  of 
100  up  to  200  feet  for  loading  E  50. 


Fig.   188.     Plates  and  Riveting  at  Upper 
End  of  End-Post. 


234 


BRIDGE  ENGINEERING 


TABLE  XXVI 
Pins  for  Sing!e=Track  Bridges 

Loading  E  50 


DIAMETER  OF  PIN 


17,  and  L0 

All  Others 

100  feet 

4i  inches 

4    inches 

125  " 

54      " 

5 

150  " 

6J       " 

5*       " 

175  " 

6|        " 

51       » 

200  " 

7 

6 

For  E  40  loading,  decrease  the  above  values  by  \  inch;  for  E  30  loading, 
decrease  them  by  £  inch.  The  diameter  of  pins  for  spans  not  given  in  the 
table  can  be  interpolated  from  the  given  values.  No  pin  should  be  less  than 
34  inches  in  diameter. 

The  span  of  this  bridge  is  147  (say  150)  feet,  and  the  diameter 
of  the  pins  at  U^  and  L0  is  6-£  —  |  =  6j  inches;  and  the  diameter 
of  the  pins  at  the  other  panel  points  is  51  —  |  =  5  inches.  It 
should  be  noted  that  no  pin  is  required  at  point  Lv  as  the  two  mem- 
bers which  join  here  are  built-up  members  and  are  riveted  together. 

The  above  table  is  for  single-track  bridges  only.  The  diameters 
of  pins  for  double-track  bridges  are  given  in  Table  XXVII.  These 
values  are  for  E  50  loading;  and  for  E  40  and  E  30  loading,  deduc- 
tions must  be  made  as  required  in  the  case  of  Table  XXVI. 

TABLE  XXVII 
Pins  for  Double-Track  Bridges 

Loading  E  50 


DIAMETER  OP  PIN 


E/,  and  L0 

All  Others 

100  feet 

6    inches 

51  inches 

125  " 

8 

64       " 

150  " 

9 

74      " 

175  " 

91-       " 

-       81       " 

200  " 

94      " 

84 

No  pin  in  a  double-track  bridge  should  be  less  than  4J  inches  in  diameter. 

Pins  for  highway  bridges  are  usually  much  less  in  diameter  than 
those  for  railway  bridges,  except  in  the  case  of  first-class  trusses  for 
heavy  interurban  traffic  or  for  city  bridges  carrying  paved  streets^ 


244 


BRIDGE  ENGINEERING 


235 


where  they  should  be  taken  equal  to  those  given  for  E  30  loading. 
Table  XXVIII  gives  the  diameters  of  pins  for  different  length  spans 
of  simple  highway  bridges  designed  for  16-ton  road-rollers  or  farm 
wagons  and  100  pounds  per  square  foot  of  roadway. 

TABLE  XXVIII 
Pins  for  Country  Highway  Bridges 

DIAMETER  OF  PIN 


17,  and  Lower  Chord 

Upper  Chord 

50  feet 
100  " 
150  " 
200  " 

2i  inches 
3"       " 

f  :: 

2    inches 
2i        " 
2|        " 
3 

89.     The  Portal.     In  order  to  have  a  clearance  of  21  feet  (2) 
above  the  top  of  rail,  it  is  necessary  that  the  portal  be  as  shown  in 
Fig.  189.  The  stresses  are  found 
by  methods  of  Article  54,  Part  I, 
the  wind  load  being  computed 
according  to  (10).     It  must  be 
remembered  that  the  column  is 
hinged. 

In  case  the  members  of  the 
portal  braces  bend  about  one 
axis,  their  length  will  be  equal 
to  the  distance  from  one  end  to 
the  other.  In  case  they  bend 
about  the  other  axis  as  indicated 
by  the  broken  line  in  Fig.  189, 
their  length  will  be  one-half  of 
what  it  was  in  the  first  case. 

The  portal  struts  or 
diagonals  will  be  designed  first. 
Their  length  is  8.5  X  1.414  - 
12  feet,  or  144  inches.  This  is 
the  total  length.  Although 
the  Specifications  do  not  men- 
tion it,  the  ratio  of  the  length  to  the  radius  of  gyration  should 
not  exceed  120.  This  means  that  the  radius  of  gyration  in  this 


Fig. 


Portal  Dimension  and  Stress 
Diagram. 


245 


236  BRIDGE  ENGINEERING 

144 
case  should  be  greater  than— -  =  1.2.     The  section  of  the  strut  will 

be  composed  of  two  angles  placed  back  to  back. 

Two  angles  3^  by  3  by  f- inch,  with  an  area  of  4.6  square  inches 
and  r2  equal  to  1 . 72 — see  Carnegie  Handbook,  p.  146,  and  (72) — will 
be  assumed  to  be  sufficient  to  take  the  stress,  and  they  must  now  be 
examined  to  see  if  the  assumption  is  correct. 

The  allowable  unit-stress  (23)  is  25  per  cent  greater  than  in  the 
case  of  live  or  dead  loads.  This  makes  the  unit-stress  as  computed 
from  the  formula: 

P  =  AG  000  -  70  X  ^7j)  It  =  12  68°  pounds  per  square  inch. 

38  500 
The  required  area  is  — — -     =  3 . 05  square  inches ;  and  since  this  is 

\-Zt  DoU 

less  than  the  given  area,  the  angle  will  be  amply  sufficient.  The  re- 
quired area  is  over  one  square  inch  less  than  the  given  area,  but  this 
angle  must  be  used,  since  it  is  the  smallest  angle  allowed  by  the  Specifi- 
cations. Note  that  unequal  legged  angles  should  be  used,  as  this  will 
make  the  radius  of  gyration  about  one  axis  larger  than  about  the  other; 
and  this  will  prove  economical,  since,  when  one  axis  is  considered, 
the  length  of  the  member  is  greater  than  when  the  other  is  considered. 
The  above  angle  should  also  be  examined  for  tension,  it  being 
considered  that  one  rivet-hole  is  taken  out  of  the  section  of  each  angle. 
The  net  section  of  the  two  angles  will  now  be  4.60  —  2  (£  +  £)  X  § 

38  500 
=  3 . 85  square  inches ;  and  the  area  required  for  tension  is  T^y- r 

=  1 .93  square  inches,  which  shows  that  the  angle  is  amply  sufficient. 
It  should  be  noted  that  these  Specifications  do  not  require  that  only 
one  leg  of  the  angle  shall  be  efficient  unless  both  legs  are  connected.  In 
case  this  strut  had  been  designed  according  to  Cooper's  Specifica- 
tions, two  angles  5  by  3  by  |-inch  would  have  been  required,  and  the 
5-inch  leg  would  have  been  placed  vertically  and  the  angle  connected 
by  this  leg  alone.  While  it  is  not  within  the  province  of  this  work  to 
discuss  the  question  of  connecting  angles  by  one  or  by  both  legs,  yet 
it  might  be  said  that  tests  made  on  angles  connected  with  one  leg 
only,  seem  to  indicate  that  the  ultimate  strength  in  tension  is  about 
60  per  cent  of  that  obtained  from  the  same  angle  when  tested  with 
both  legs  connected. 


246 


BRIDGE  ENGINEERING  237 

While  according  to  (20)  the  alternate  strains  in  the  wind  bracing 
do  not  have  to  be  considered,  since  they  do  not  occur  very  closely 
together,  yet  in  framing  the  connections  it  is  required  that  the  sum  of 
both  positive  and  negative  stresses  shall  be  added.  In  this  case  the 
stress  for  which  the  connections  must  be  designed  is  2  X  38500 
=  77  000.  It  must  be  remembered  that  in  this  case  also,  the 
unit-stresses  are  increased  25  per  cent  over  those  allowed  for  live  and 
dead  loads. 

The  number  of  rivets  required  in  the  end  connections  will  be 
governed  by  bearing  in  the  connection  plates,  and  these  plates  are 
usually  made  f-inch  thick.  The  number  of  rivets  required  is 

77  000  77  000 

7-880^0*  -  8  Sh°P  metS'  °r  6560-YU  = 

The  portal  bracing  is  riveted  up  in  the  shop  and  brought  to  the 
bridge  site,  where  it  is  connected  to  the  trusses  by  field-riveted  con- 
nections at  its  end.  Therefore  the  end  of  the  portal  struts  which 
connect  with  the  top  piece  will  have  8  shop  rivets,  and  the  other  end 
which  connects  with  the  end-post  will  have  10  field  rivets.  Since 
the  angles  are  small,  all  the  above  rivets  must  go  in  one  line,  and  this 
will  cause  the  connection  plate  to  be  quite  large.  It  will  probably  be 
better  to  connect  both  legs  of  the  angle  by  means  of  clip  angles  and 
thus  reduce  the  size  of  the  connection  plates. 

The  top  part  of  the  portal  bracing  will  consist  of  two.  angles. 
Two  angles  3-j  by  3  by  f-inch  will  be  assumed  and  examined  to 
determine  if  the  area  is  sufficient.  The  length  of  this  strut  is  the 
distance  center  to  center  of  trusses,  and  is  equal  to  17  X  12  =  204 

^04 
inches.     The  least  radius  of  gyration  is  therefore  ~—  -  =  1  .  70.     The 

radius  of  gyration  of  the  two  angles  assumed  is  1  .  72  when  referred  to 
an  axis  parallel  to  the  shorter  leg  when  the  two  angles  are  placed  back 
to  back  and  One-half  inch  apart.  The  unit-stress  is  now  computed: 

(9Q4  \ 
16  000  -  70  X  Y~^)  H  =  9  625  pounds  per  square  inch. 

27  200 
The  required  area  is^-^-  =  2.825  square  inches.     This  is  con- 


siderably  less  than  the  area  given  by  the  two  angles;  but  as  these  are 
the  minimum  angles  allowable,  they  must  be  used.  Since  the  stress 
in  this  case  is  less  than  in  the  previous  -case,  and  since  the  angles 


247 


238 


BRIDGE  ENGINEERING 


used  are  the  same,  it  is  evident  that  these  angles  are  safe  in  tension. 
The  number  of  rivets  is  determined  by  the  bearing  in  the  f-inch 
connection  plates,  and  is : 

2  X  27  200 


7  880  X  1 . 25 
2  X  27  200 
6560  X  1.25 


=     6  shop  rivets,  and 


=  10  field  rivets. 


As  in  the  case  of  the  lateral  strut,  this  member  should  be  connected 
by  both  legs  of  the  angle  in  order  to  reduce  the  size  of  the  connection 

plates.  Fig.  190  gives  the 
details  of  the  portal  bra- 
cing and  its  method  of 
connection  to  the  end- 
post.  The  full  circles 
represent  shop  rivets,  and 
the  blackened  circles  rep- 
resent field  rivets.  Some 
engineers  connect  the 
portal  bracing  to  the  top 
cover-plate  of  the  end- 
post.  This  produces  an 
excessive  eccentricity  in 
the  end-post  and  is  bad 
practice. 

Those  members  of  the  portal  bracing  which  do  not  take  any 
stress  will  be  made  of  single  angles,  and  the  size  of  these  angles  will  be 
taken  3$  by  3  by  f-inch. 

90.  The  Transverse  Bracing.  This  bracing  will  be  the  same 
general  style  as  the  portal  bracing,  except  that  the  top  member  will 
consist  of  two  angles  placed  at  a  distance  apart  equal  to  the  depth 
of  the  top  chord,  and  these  angles  will  be  joined  together  by  lacing. 
As  in  the  case  of  portal  bracing,  those  members  which  do  not  take 
stress  will  be  made  of  one  angle  3|  by  3  by  f-inch. 

The  general  outline  is  shown  in  Fig.  191,  and  the  stresses  are  com- 
puted from  (10)  and  by  the  methods  of  Article  54,  Part  I.  In  design- 
ing this  top  member,  the  top  angle  only  is  supposed  to  take  the  stress. 
The  length  in  this  case  is  204  inches.  Two  34  by  3  by  f-inch  angles 
will  be  assumed  as  sufficient  and  will  be  examined.  These  angles 


Pig.  190.    Details  of  Portal  Bracing  and  Connection 
to  End-Post. 


248 


BRIDGE  ENGINEERING 


239 


give  a  total  area  of  4.60  square  inches.  In  examining  these  it  will 
be  found  that  they  are  amply  sufficient,  in  fact  so  much  so  that  it  will 
be  better  to  see  if  one  single  angle  at  the  top  will  not  be  better. 
According  to  the  length,  the  smallest  radius  of  gyration  which  can  be 
used  is  1.7.  In  looking  over  the  tables  of  angles,  it  is  seen  that  the 


T.|.9«*" 

-ii 

Oil 


T-126" 

Hi 


Section 


Fig.  191.    General  Outline  of  Transverse  Bracing. 

first  angle  to  fulfil  this  condition  is  a  6  by  3^  by  f-inch,  and  it  has  a 
radius  of  gyration  of  1.94.  The  allowable  unit-stress  is  computed 
as  follows: 

P  =  (l6  000  -  70  X  p^)H  =  10  780  pounds  per  square  .inch; 

9  100 
and  the  required  area  is        ™  =  0.85  square   inch.      This  is  con- 


249 


240 


BRIDGE  ENGINEERING 


siderably  smaller  than  the  area  of  the  angle,  which  is  3.97  square 
inches;  but  since  this  is  the  smallest  possible  angle  which  will  fulfil 
the  conditions  of  the  Specifications,  and  since  it  is  much  smaller  than 
the  two  angles  as  first  assumed,  it  will  be  used.  Fig.  192  gives  a  cross- 
section  of  this  member.  Since  this  angle  is 
joined  to  the  cover-plate  by  one  leg,  the  joints 
will  be  weak  in  single  shear,  and  the  number  of 
rivets  required  will  be: 


X  9  100 


=  2  shop  rivets,  or 


6013  X  1J 


=  3  field  rivets. 


According  to  (45),  the  width  of  the  latticing 
must  be  24  inches  ;  and  according  to  Table  XXV, 
the  thickness  must  be  -j7s  inch,  the  distance  c  be- 
ing 1  foot  11  inches. 

The  length  of  the  knee-bracing  is  144  inches; 
but  on  account  of  the  small  stress,  one  angle  will 

,  ,    i        «   i  -    «  .      T 

be  used.     One  4  by  3  by  f-inch  angle,  with  an 

.      , 

area  of  2  .  48  square  inches  and  a  radius  of  gyra- 
tion 1.26,  will  be  assumed  as  sufficient.  The  radius  of  gyration 
is  greater  than  the  minimum  allowable,  which  is  1.2.  The  allowable 
unit-stress  is: 


Fig.  192.     Cross-  Sec- 

tion  of  Top  Member  of 

Transverse  Bracing. 


1C  000  -  70  X 


The  required  area  is 


12300 


10  000  pounds  per  square  inch." 


=  1.23  square  inches.     The  required 


area  is  much  less  than  the  given  area;  but  this  angle  must  be  used, 
since  it  is  the  only  one  allowed  on  account  of  its  radius  of  gyration. 
Two  of  the  minimum  sized  angles  might  have  been  used;  but  their 
total  area,  4.60  square  inches,  is  much  in  excess  of  that  of  the  angle 
used. 

This  angle  must  be  examined  for  tension.    The  net  area  is  2.48 
~(i  +  i)Xf  =  2.1  square    inches.    The    required    net   area   in 

12  300 

tension  is——     — —  =  0.615  square  inch,  which  shows  this  angle 
lo  000  X  lj 

to  be  amply  sufficient. 


250 


BRIDGE  ENGINEERING 


241 


The  number  of  rivets  required  will  be  governed  by  the  shear, 
since  the  angle  is  connected  by  one  leg  only;  and  it  is: 

2  X  12  300 
7  220  X 

2  X  12  300 


91.  The  Lateral  Systems.  The  stresses  in  these  systems  must 
be  computed  according  to  (10)  and  Article  54,  Part  I.  They  are  given 
on  the  stress  sheet,  Plate  III  (p.  251).  Since  according  to  (68)  these 
members  must  be  constructed  of  rigid  shapes,  it  is  customary,  in  com- 
puting the  stresses,  to  assume  that  one-half  the  shear  is  taken  by  each 
of  the  diagonals  in  any  given  panel;  that  is,  one  diagonal  is  in  tension, 
and  the  other  diagonal  is  in  compression.  The 
stresses  given  on  the  stress  sheet  are  computed 
by  making  this  assumption.  Also,  since  both 
diagonals  in  each  panel  are  considered  as  acting 
at  the  same  time,  the  stresses  in  all  the  verticals 
are  zero. 

The  section  of  the  upper  lateral  members  will 
be  made  up  of  two  angles  placed  apart  a  distance 
equal  to  the  depth  of  the  top  chord.  Fig.  193 
shows  the  section.  The  radius  of  gyration  about 
the  axis  parallel  to  the  long  leg  will  be  consider- 
ably larger  than  that  about  an  axis  parallel  to  the 
shorter  leg.  In  fact,  it  is  so  much  greater  that  the 
strut  will  not  need  to  be  examined  with  respect 
to  this  axis.  The  diagram  of  the  first  panel  is 
given  in  Fig.  194.  The  radius  of  gyration  is  to  be  taken  about 
the  horizontal  axis  if  the  entire  length  is  to  be  taken;  and  the  radius 
of  gyration  is  to  be  taken  about  the  vertical  axis  if  one-half  the 
length  is  taken,  in  which  case  it  will  bend  as  shown  by  the  broken 
line  in  Fig.  194.  The  members  are  designed  for  the  latter 
conditions  only,  since  they  are  amply  safe  in  regard  to  the  first 
condition  if  they  satisfy  the  latter.  The  length  in  this  latter  con- 
dition is  13.5  feet,  which  requires  a  radius  of  gyration  not  less  than 
13.  5  X  12 


Fig, 


Upper  Lateral 
Men 


120 


1.35. 


Two  angles  5  by  3  by  f-inch,  with  a  total  area  of  5 . 72  square 


251 


242 


BRIDGE  ENGINEERING 


inches  and  a  radius  of  gyration  equal  to  1.61,  will  be  assumed  and 
investigated  to  determine  if  they  are  sufficient. 

1  o  c  y  -to 
The  unit-stress  is  computed  to  be  P  =  (16  000 - 70  X     '     p.—)  X 

n  nr\c\ 

1 J  =  11  000  pounds  per  square  inch,  and  the  required  area  is———  = 

1 1  UUU 

0.61  square  inch.  The  required  area  is  very  much  less  than  the 
given  area;  but  the  angle  chosen  must  be  used,  since  this  is  the 
smallest  one  which  conforms  to  the  requirements  of  the  Specifications. 


Fig.  194.    Outline  Diagram  of  First  Panel 
in  Upper  Lateral  System. 


Fig.  195.    Outline  Diagram  of  First  Panel 
in  Lower  Lateral  System. 


The  width  of  the  lattices  (46)  must  be  2|  inches;  and  according 
to  Table  XXV,  the  thickness  must  be  •&  inch,  the  distance  c  being 
23  inches. 

Single  shear  governs  the  number  of  rivets  required.  In  accord- 
ance with  (20)  and  (23),  their  number  is —  —=  2  rivets.  Field 

6  013  X  1 5 

rivets  3  in  number  are  used  in  all  places,  since  the  lateral  system  is 
riveted  up  after  the  trusses  are  swung  into  place. 

Since  this  is  the  minimum  sized  angle  which  will  give  a  radius  of 
gyration  greater  than  1 . 35,  it  must  be  used  in  the  remainder  of  the 
panels  of  the  top  chord.  Four  angles  of  the  minimum  size  might 
have  been  used,  and  would  have  been  satisfactory,  except  that  the 
area  would  have  been  excessive. 

The  stresses  in  the  lower  lateral  system  are  computed  according 
to  (10),  a  similar  assumption  to  that  for  the  upper  lateral  system  being 
made — namely,  that  both  diagonals  in  each  panel  are  stressed  at  the 
same  time,  one  taking  tension  and  the  other  taking  compression. 
Fig.  195  shows  the  first  panel  of  the  lower  lateral  system.  These 


252 


BRIDGE  ENGINEERING  243 

diagonals  are  connected  to  the  stringers  wherever  they  cross  them, 
and  also  to  each  other  where  they  cross  in  the  center.  This  reduces 
the  length  which  must  be  used  in  computing  the  cross-section  of  the 
member.  In  this  case  it  is  the  distance  C-A,  and  is  equal  to  90  inches. 
Since  the  angle  is  free  to  move  about  either  axis,  angles  with  even 
legs  should  preferably  be  employed,  since  this  will  give  greater 

90 
economy.     The  radius  of  gyration  must  be  greater  than  —  —  =  0  .  75. 

One  angle  3  1  by  3^  by  f-inch,  with  an  area  of  2  .48  square  inches 
and  a  radius  of  gyration  of  1.07,  will  be  assumed  and  investigated. 

00 
The  allowable  unit-stress  is  P  =  (16  000  -  70  X  —  )  H  =  12650 

on  C:AQ 

pounds  per  square  inch,  and  the  required  area  is  =  2  .  38  square 

\2i  boO 

inches.     This  is  nearly  equal  to  the  given  area,  and  therefore  the 
angle  chosen  will  be  taken  for  the  section. 

This  angle  must  now  be  investigated  for  tension,  one  rivet-hole 
being  taken  out  of  the  section.     The  net  area  is  2.48  —  (f  +  £)  f  = 

SO  500 

2.10  square  inches.     The  required  net  area  is——     —  -y  =1.53 

i  u  (JUU  X   J-  X 

square  inches,  which  shows  the  angle  to  be  sufficiently  strong. 

Single  shear  determines  the  number  of  rivets  to  be  required. 
These  are: 


All  rivets  in  the  lower  lateral  system  are  field  rivets,  since  this  system 
also  must  be  riveted  up  in  the  field  after  the  trusses  are  swung  into 
place. 

The  total  stress  in  the  second  panel  is  21  500  pounds,  and  a 
3^  by  3  by  f-inch  angle,  with  an  area  of  2.30  square  inches  and  a 
least  radius  of  gyration  of  0  .  90,  will  be  assumed  and  examined.  The 

90 
allowable  unit-stress  in  compression  is  \\  (16  000  —  70  X          )  = 

21  500 
1  1  250  pounds  per  square  inch,  and  the  required  area  is  =  1  .  91 

1  1  ^-£)U 

square  inches.  Since  this  is  less  than  the  given  area,  and  since  the 
size  of  the  angle  (72)  is  the  smallest  allowable,  this  angle  must 
be  used. 


253 


244 


BRIDGE  ENGINEERING 


It  is  required  that  this    member    shall    have    a    net    area  of 

21  500 

1.08  square  inches  in  tension.     The  net  area  of  the 


16  000  X 

angle,  one  rivet-hole  being  taken  out,  is  1.92  square  inches,  which 

shows  the  angle  to  be  safe  in  tension. 

The  number  of  rivets  required  is  determined  by  single  shear, 


Fig.  196.    Two  Types  of  Hearings. 

since  they  tend  to  shear  off  between  the  member  itself  and  the  con- 


necting  plates.      The  number  required  is  — 


500 


0013  XH 

Since  the  above  angle  is  the  smallest  that  can  be  used,  and  since 
the  remaining  angles  of  the  panel  of  the  lateral  bracing  have  smaller 
stresses  than  the  one  just  designed,  it  is  evident  that  this  size  angle 
must  be  used  in  all  panels  of  the  lower  lateral  system  other  than  the 
first. 

92.  The  Shoes  and  Roller  Nests.  For  bridges  of  short  spans 
and  for  plate-girders  whose  spans  require  rocker  bearings  to  be  pro- 
vided (80),  several  different  classes  of  bearings  are  in  use.  Two  such 
bearings  are  shown  in  Fig.  196  (a  and  6).  The  type  illustrated  by  a 
is  seldom  used  on  any  spans  except  plate-girders.  That  shown  in  b 


254 


BRIDGE  ENGINEERING 


245 


may  be  used  on  either  plate-girders  or  small  truss  spans;  it  is  the 
invention  of  Mr.  F.  E.  Schall,  Bridge  Engineer  of  the  Lehigh  Valley 
Railroad,  who  uses  it  on  plate-girders.  It  has  given  very  great  satis- 
faction; and  for  simplicity  of  design  and  also  for  economy  it  is  to  t)e 
recommended.  Some  railroads  have  used  a  bearing  which  consisted 
of  a  lens-shaped  disc  of  phosphor-bronze,  the  faces  of  which  fitted 
into  corresponding  indentations  in  both  the  masonry  and  the  bearing 
plates.  One  advantage  of  this  bearing  is  that  it  allows  movements 
due  to  the  deflection  of  the  girder,  and  also  lateral  deflection  of  the 
floor-beam.  It  is  claimed  to  have  given  satisfaction. 

A  bearing  which  is  used  on  both  short-span  and  long-span  bridges 


Fig.  197.    Bearing  Adapted  to  Bridges  of  Both  Short  and  Long  Span. 

is  shown  in  Fig.  197.     This  class  of  bearing  will  be  used.     The  end 
reaction  of  the  bridge  proper  is  equal  to  the  vertical  component  of  the 

30  1 
stress  in   the  end-post,  and  is  ^— —  X  410  500  =  336  500  pounds, 

336  500 
which  requires  a  bearing  area  (19)  on  the  masonry,  ot    '       — =•  561 

square  inches.     According  to  the  table  on  page  193,  the  masonry 
plate  will  be  28  inches  long. 

The  total  bearing  area  for  one  of  the  vertical  plates  is : 


255 


246  BRIDGE  ENGINEERING 

and  the  total  required  thickness  is: 

7.0 

-  0,  =  1 . 12  inches, 

6.2o 

a  6  j-inch  pin  being  used  at  L0.  Since  the  vertical  plates  will  be  made 
f  inch  thick,  this  leaves  a  remainder  of  f  inch  to  be  made  up  of  pin- 
plates. 

The  amount  of  stress  which  is  carried  by  the  f-inch  pin-plate  is 

n  *?7^      ^*^fi  ^oo 

-^  X      "         =  56  100  pounds.     These  plates  will  tend  to  shear 

56  100 
off  the  rivets  at  a  plane  between  the  plates,  and  therefore  =  8 

shop  rivets  will  be  required  to  fasten  them  to  the  vertical  plate. 

Since  the  length  of  the  masonry  plate  is  28  inches,  and  the  total 

561 
area  required  is  561  square  inches,  the  required  width  is  =  20 

inches.  The  actual  width  will  be  greater  than  this,  since  it  must  be 
sufficient  to  allow  for  the  connecting  angles  and  also  for  the  bearings 
of  the  end  floor-beam.  The  connecting  angles  should  be  f  inch  thick, 
and  should  not  be  less  than  6  by  6  inches;  and  the  plates  to  which  they 
are  connected  should  not  be  less  than  f  inch  in  thickness,  and  likewise 
they  should  not  be  greater,  on  account  of  the  punching.  The  bottom 
plate  should  extend  outward  about  3  inches,  in  order  to  allow  suf- 
ficient room  for  the  anchor  bolts,  which  should  be  f  inch  in  diameter 
and  should  extend  into  the  masonry  at  least  8  inches. 

In  addition  to  the  reaction  of  the  bridge  proper,  the  masonry 
plate  must  be  of  sufficient  area  to  give  bearing  for  the  end  reaction  of 
the  end  floor-beam.  The  maximum  end  reaction  (see  Article  83,  p. 
197)  is  104  740  pounds.  The  bearing  area  required  on  the  masonry 

104740 

is  — — — — =  17o  square  inches;  and  assuming  that  the  base  of  the 
600 

bearing  will  be  12  inches  long  (see  Fig.  197),  the  required  length  will 
be  14.6  inches.  Usually,  however,  the  bearing  is  extended  the  entire 
length  of  the  masonry  plate,  which  is  28  inches  in  this  case. 

The  distance  from  the  center  of  the  pin  to  the  top  of  the  masonry 
will  be  the  same  for  both  the  fixed  and  the  roller  end.  This  distance 
should  be  such  that  the  angles  of  the  shoe  will  clear  the  bottom  chord 
member  and  allow  the  floor-beam  to  rest  upon  the  plate  as  shown. 
Since  the  first  section  of  the  bottom  chord  is  18$  inches  deep,  the  top 
of  the  angles  of  the  two  must  be  at  least  9|  inches  from  the  center  line 


256 


BRIDGE  ENGINEERING 


247 


of  pins.  This  requires  that  the  distance  from  the  center  line  of  the 
pin  to  the  base  of  the  angle  shall  be  at  least  (9j  +  6)  =  15J  inches, 
or  more. 

The  tops  of  all  floor-beams  are  at  the  same  height,  and  the 
bottoms  of  the  intermediate  floor-beams  must  be  on  a  level  with  the 
bottom  of  the  first  section  of  the  lower  chord  (see  Fig.  174).  This 
requires  that  the  bottom  of  the  intermediate  floor-beams  shall  be 
9^  inches  below  the  center  line  of  pins,  and  this  brings  the  top  of  the 
floor-beams  (4S-J-  —  9|)  =  39  inches  above  the  center  line  of  the  pins. 
Since  the  end  floor-beam  is  52 \  inches  deep,  back  to  back  of  angles,  the 


hijj 

6uld5-.pi^ 

Seqmzntal  Kollew  eV^a"                      llflh 
Guide  Bars  ej-ifj  If  i-L  s"*3  i"* 

f|Cho,BoU  * 
,, 

II 

U  1 

Lsa: 

Fig.  198.    Type  of  Bearing  Construction  where  End  Floor-Beam  Does  Not  Rest  Directly  on 
Bearing  or  Masonry  Plate.    Grillage  of  Iron  Bars  Used  instead  of  Cast-Steel  Pedestal. 

lower  flange  will  be  (52f  —  39)  =  13|-  inches  below  the  center  line  of 
pins.  In  case  the  end  floor-beam  does  not  rest  directly  upon  the 
bearing  plate  or  the  masonry  plate,  the  intervening  space  is  filled  out 
with  a  grillage  of  iron  bars  or  a  cast-steel  pedestal,  as  shown  in  Figs. 
197  and  198. 

The  small  plates  upon  the  side  of  the  shoe,  going  entirely  around 
the  pin,  are  called  the  shoe  hinge-plates.  These  do  not  take  any  stress, 
and  require  only  sufficient  rivets  to  hold  them  in  position.  They  are 
used  during  erection  to  keep  the  end-post  in  line;  and  after  erection 
their  function  is  to  keep  the  end-post  on  the  shoe,  and  to  prevent  it 
from  having  any  upward  motion  due  to  the  vibration  of  the  structure. 


257 


248  BRIDGE  ENGINEERING 

The  rivets  through  the  vertical  legs  of  the  shoe  angles  are  in 
double  bearing  in  the  f-inch  angles,  in  single  bearing  in  the  vertical 
plate,  and  in  double  shear.  A  rivet  in  double  shear  has  a  less  value 
than  in  bearing  in  the  plates.  This  value  is  14440  pounds,  and 
therefore  the  number  of  shop  rivets  required  through  the  vertical  legs 
of  the  angles  is : 

336  500 


2  X  14  440 


=  12  rivets. 


The  rivets  which  go  through  the  horizontal  leg  of  the  angle  and 
through  the  cap  plate  and  cap  angles,  do  not  take  stress.  The  num- 
ber of  rivets  put  in  is  that  demanded  by  the  detailing,  the  rivets  in  the 
horizontal  legs  of  the  angles  usually  staggering  with  those  in  the  verti- 
cal legs.  The  cap  plate  tends  to  keep  the  vertical  plates  in  line,  and 
to  keep  out  the  dust  and  dirt  and  other  deteriorating  influences  of 
the  elements. 

Wherever  the  rivet-heads  tend  to  interfere  with  other  members 
or  project  beyond  surfaces  which  are  required  to  be  flat — as,  for 
example,  the  bottom  of  the  masonry  or  bearing  plates — they  must  be 
countersunk  (see  Carnegie  Handbook,  p.  191,  and  "Steel  Construc- 
tion," Part  III,  p.  192). 

The  space  for  the  anchor  bolts,  that  for  the  connection  angles, 
and  that  for  the  bearing  of  the  end  floor-beam,  require  that  the  total 
width  of  the  masonry  plate  for  the  fixed  end  shall  be  2  X  f  +  14^  +  2 
X  6  +  \  +  3  +  12  =  3  feet  1\  inches. 

The  design  of  the  roller  end  requires  that  the  length  of  the 
masonry  bearing,  the  size  of  the  vertical  plates  and  angles,  and  also 
the  number  of  rivets  shall  be  the  same  as  that  for  the  fixed  end.  The 
width  of  the  masonry  plate  is  determined  by  the  length  of  the  rollers 
and  their  connections  at  the  end. 

The  rollers  (60)  are  required  to  be  6  inches  in  diameter,  and  the 
unit-stress  (19)  per  linear  inch  is  6  X  600  =  3  600  pounds,  which 
requires : 

336  500 

0  gf.-     =  93 . 5  linear  inches. 
6  600 

This  is  for  the  reaction  of  the  bridge  alone;  and  in  addition  to  this, 
there  are  required  for  the  floor-beam  reaction : 

r-  =  29.0  linear  inches. 


858 


BRIDGE  ENGINEERING 


249 


The  total  number  of  linear  inches  is  93.5  +  29.0  =  122. 5;  and  if  5 

rollers  are  used,  they  must  be  at  least  — -^-  =24.5  inches  long.  The 

5 

masonry  plate  is  only  28  inches  long,  and  therefore  cylindrical  rollers 
cannot  be  used,  since  they  would  occupy  a  space  30  inches  or  over. 
Segmental  rollers  (see  Fig.  199) 
must  be  used. 

The  determination  of  the 
sizes  of  the  angles  which  go  at  the 
end  of  the  rollers,  and  also  of  the 
guide-plates,  is  a  matter  of  judg- 
ment and  experience.  Those 
sizes  indicated  in  Fig.  198,  repre- 
sent good  engineering  practice, 
and  will  be  used. 

The  distance  from  the  center 
line  of  pins  to  the  top  of  the  ma- 
sonry can  now  be  determined, 
and  is  16J  +  |  +  6  +  |  =  23| 
inches. 

On    account    of    putting   in    Fig.  199.    Segmental  Rollers  Used  for  Deal- 
ings in  Space  under  30  Inches. 

sufficient  connections  and  angles 

as  shown  in  Fig.  198,  the  masonry  plate  must  be  considerably  wider 
than  that  theoretically  determined.  According  to  Fig.  198,  the  total 
width  must  be  as  follows,  and  the  width  should  be  computed  in  two 
parts,  as  the  plate  is  not  symmetrical  about  the  center  line  of  the  truss: 
From  center  line  to  outer  edge: 

^  +  \  +  6  +  *  +  (3  -  f  =  2f )  +  (3*  -  f  =  3|)  +  3 

=  1  ft.  Hi  in.,  (say,  1  ft.  11  in.). 
From  center  line  to  inner  edge: 

—2  +  i  +  6  +  1  +  12  +  *  +  2£  +  3i  +  3  =  3  ft.  Oi  in.,  say,  3  ft.    0  in. 


Total   width  4ft.  11  in. 

Allowing  guide-plates  and  guide-bars  of  dimensions  as  shown  in 
Fig.  198,  and  assuming  ^  inch  as  clearance  at  the  ends,  the  total  length 
of  the  rollers  is: 

(4  ft.  11  in.  )  -  2  (3  +  3*  +  J  +  J  +  $)  =  44.  5  inches. 
This  shows  them  to  be  amply  long  enough,  as  only  22  inches  is 


259 


250  BRIDGE  ENGINEERING 

theoretically  required.  Here,  as  in  most  cases  for  single-track  spans 
up  to  200  feet  in  length,  the  width  of  the  masonry  plate  is  determined 
by  the  detail  and  not  by  the  unit  bearing  stress. 

The  guide-plates  are  small  bars  riveted  to  the  top  of  the  bottom 
plates,  and  serve  to  keep  the  rollers  in  line.  The  guide-bars  are  con- 
nected to  rollers  at  their  ends,  and  serve  to  keep  the  rollers  equi- 
distant, therefore  causing  them  to  roll  easier  and  keeping  them  from 
becoming  worn  by  contact  with  each  other. 

The  expansion  (57)  must  be  allowed  for  at  the  rate  of  |  inch  for 
every  10  feet  in  length  of  span.  This  makes  a  total  allowed  for  tem- 
perature of  expansion  of  -.---  X  I •  =  If  (say  2)  inches.  No  slotted 
holes  are  to  be  provided  for  the  anchor  bolts,  since  they  do  not  go 


I ' 

Fig.  200     Binding  of  Insufficiently  Spaced       Fig.  201.    Computation  of  Spacing  for  Seg- 
Segmental  Rollers.  mental  Rollers. 


through  that  part  of  the  bridge  which  slides.  The  shoe  slides  over 
the  rollers,  and  is  kept  in  place  by  the  angles  at  the  end,  which  are 
riveted  to  the  masonry  plate  (see  Fig.  198). 

Unless  sufficient  room  is  allowed  between  the  segmental  rollers, 
they  will  tend  to  bind  when  the  bridge  has  reached  the  extreme  posi- 
tion for  expansion  or  contraction  (see  Fig.  200).  This  distance  can  be 
computed  from  proportions  as  indicated  in  Fig.  201,  and  from  the 
following  formuhe*: 


in  which  e  is  the  amount  allowed  for  the  change  of  temperature,  and 
D  is  the  diameter  of  the  rollers,  both  being  taken  in  inches.  The 
angle  <£  is  in  degrees.  In  the  present  case,  eis2  inches;  D  is  6  inches; 


*  Derived  by  Prof.  Frank  B.  McKibben  of  Lehigh  University,   and  published  in 
Engineering  News,  December,  1896. 


252 


BRIDGE  ENGINEERING 


and  (f>,  computed  from  the  above  formula,  is  9°  30'.  Substituting  in 
the  equation  giving  the  value  for  y,  there  is  obtained  1 .02  inches  (say 
\\  inches)  for  the  distance  between  rollers.  Rollers  must  not  be  less 
in  thickness  than  the  total  expansion  allowed  for  temperature. 

Since  there  are  5  rollers,  there  are  4  spaces  between  them.  Also, 
since  the  rollers  must  occupy  a  space  of  28  inches,  the  length  of  the 
masonry  plate,  each  roller  must  be: 

— - —  —  =  4.6  inches  (say  4£  inches)  wide. 
The  width  of  the  guide-bars  must  be  such  as  to  allow  freedom 


Fig.  202.    Details  of  End  Floor-Beam  Connections. 

of  motion  for  the  rollers.     The  maximum  width  allowable  is  given  by 
the  formula  :* 


in  which  </>  and  D  are  indicated  above.     This  requires  the  bar  to  be . 

W  =  -|-  X  0 . 985  =  2 . 96  (say  24)  inches  wide. 

93.  The  Stress  Sheet.  Plate  III  shows  the  stress  sheet  of  the 
bridge  which  has  been  designed  in  the  preceding  articles.  This 
sheet  represents  the  best  current  practice  among  the  larger  bridge 

*  Derived  by  Prof .  Frank  B.  McKibben  of  Lehigh  University,  and  published  in 
Engineering  News,  December,  1896. 


262 


BRIDGE  ENGINEERING 


253 


corporations.  It  will 
be  noted  that  very 
few  details  are  given 
upon  the  sheet;  also 
that  few  rivets  are 
noted,  and  that 
sketches  showing  the 
manner  in  which  the 
parts  go  together  are 
entirely  wanting.  The 
shears  and  moments 
for  the  stringers  and 
floor-beams,  as  well  as 
the  reactions  and  the 
number  of  rollers  re- 
quired, are  given.  This 
is  to  save  the  drafts- 
man the  trouble  of 
recomputing  values 
which  have  necessarily 
been  determined  by 
the  designer. 

The  details  of  the 
various  members,  and 
also  -  the  manner  in 
which  the  different 
members  are  con- 
nected, are  left  to  the 
draftsman,  who  is  un- 
der the  direct  super- 
vision of  the  engineer 
in  charge  of  the  draft- 
ing room,  upon  whom 
rests  the  responsibility 
for  good  details.  The 
figures  given  in  the 
text  indicate  the  best 
current  practice.  Figs. 


i  '  «"  1 

l 

.£  § 

5s 

.  . 

1 

0 

I 

_H..J 


263 


254  BRIDGE  ENGINEERING 

202  to  204  show  details  of  the  end  floor-beam  connections,  and  also 
the  packing  of  the  members  of  the  upper  and  the  lower  chord.  The 
arrangement  here  given  may  be  said  to  be  standard  for  single-track 
Pratt  truss  spans  up  to  200  feet  in  length. 

BIBLIOGRAPHY 

The  following  books  are  recommended  to  the  student  in  case  it 
is  desired  to  pursue  further  the  study  of  the  subjects  of  Bridge 
Analysis  and  Bridge  Design : 

The  Theory  and  Practice  of  Modern  Frame  Structures.  JOHNSON; 
BRYAN,  and  TURNEAURE.  John  Wiley  &  Sons,  New  York,  N.  Y. 

Roofs  and  Bridges.  MERRIMAN  and  JACOB  Y.  John  Wiley  &  Sons,  New 
York,  N.  Y. 

Design  and  Construction  of  Metallic  Bridges.  BURR  and  FALK.  John 
Wiley  &  Sons,  New  York,  N.  Y. 

Influence  Lines  for  Bridges  and  Roofs.  BURR  and  FALK.  John  Wiley 
&  Sons,  New  York,  N.  Y. 

Details  of  Bridge  Construction.  FRANK  W.  SKINNER.  McGraw  Pub- 
lishing Company,  New  York,  N.  Y. 

Steel  Mill  Buildings.  Milo  S.  Ketchum.  Engineering  News  Publish- 
ing Company,  New  York,  N.  Y. 

Statically  Indeterminate  Stresses.  HIROI.  Engineering  News  Pub- 
lishing Company,  New  York,  N.  Y. 

Stresses  in  Frame  Structures.  A.  JAY  DuBois.  John  Wiley  &  Sons, 
New  York,  N.  Y. 

Die  Zusatzkrdfte  und  Nebenspannungen  eiscrner  Fachwerkbriicken.  FR. 
ENGESSER.  Julius  Springer,  Berlin,  Germany. 

Bridge  Drafting.  WRIGHT  and  WING.  Engineering  News  Publishing 
Company,  New  York,  N.  Y. 

It  must  not  be  presumed  that  the  above  is  a  complete  list  of  the 
books  which  have  been  published  relating  to  the  theory  and  practice 
of  Bridge  Engineering;  neither  must  it  be  presumed  that  the  obtaining 
of  information  relative  to  bridges  is  limited  to  textbooks  on  the 
subject.  One  of  the  best  sources  of  information  is  found  in  the  cur- 
rent engineering  periodicals  and  the  "Proceedings"  of  the  various 
technical  societies.  The  great  advantage  of  these  sources  is  that  they 
give  the  most  up-to-date  information,  and  usually  they  are  very  pro- 
fusely illustrated. 


264 


ROAD  CONSTRUCTION  IN  THE  PHILIPPINES 

Section  of  35-mile  road  built  by  American  engineers,  connecting  the  seaport  of  Dagupan  with 
the  mountain  village  of  Baguio.  province  of  Benguet,  island  of  Luz6n,  and  affording  a  cool  and 
healthful  retreat  from  the  heat  and  malaria  of  the  lowland  re£*ions.  Dagupan  lies  120  miles  north  of 
Manila,  with  which  it  is  connected  by  rail.  This  view  reveals  some  of  the  engineering  difficulties  to 
be  overcome,  masonry  and  concrete  work  of  the  type  shown  being  necessary  at  many  points. 


HIGHWAY  CONSTRUCTION 

PART  I. 


COUNTRY    ROADS. 

GENERAL  CONSIDERATIONS. 

Object  of  Roads.  The  object  of  a  road  is  to  provide  a  way 
for  the  transportation  of  persons  and  goods  from  one  place  to  another 
with  the  least  expenditure  of  power  and  expense.  The  facility  with 
which  this  traffic  or  transportation  may  be  conducted  over  any  given 
road  depends  upon  the  resistance  offered  to  the  movement  of  vehicles. 
This  resistance  is  composed  of:  (1)  The  resistance  offered  by  the 
roadway,  which  consists  of  (a)  "friction"  between  the  surface  of 
the  road  and  the  wheel  tires;  (6)  resistance  offered  to  ths  rolling  of 
the  wheels,  occasioned  by  the  want  of  uniformity  in  the  road  surface, 
or  lack  of  strength  to  resist  the  penetrating  efforts  of  loaded  wheels, 
thus  requiring  the  load  to  be  lifted  over  projecting  points  and  out  of 
hollows  and  ruts,  thereby  diminishing  the  effective  load  the  horse 
may  draw  to  such  as  it  can  lift.  This  resistance  is  called  "resistance 
to  rolling"  or  "penetration;"  (c)  resistance  due  to  gravity  called 
"grade  resistance;"  (2)  The  resistance  offered  by  vehicles,  termed 
"axle  friction;"  (3)  Resistance  of  the  air. 

The  road  which  offers  the  least  resistance  to  traffic  should  com- 
bine a  surface  on  which  the  friction  of  the  wheels  is  reduced  to  the 
least  possible  amount,  while  offering  a  good  foothold  for  horses,  to 
enable  them  to  exert  their  utmost  tractive  power,  and  should  be  so 
located  as  to  give  the  most  direct  route  with  the  least  gradients. 

Friction.  The  resistance  of  friction  arises  from  the  rubbing  of 
the  wheel  tires  against  the  surface  of  the  road.  This  resistance  to 
traction  is  variable,  and  can  be  determined  only  by  experiment. 
From  many  experiments  the  following  deductions  are  drawn : 

(1)  The  resistance  to  traction  is  directly  proportional  to  the 
pressure, 

Copyright,  1908,  by  American  School  of  Corespondent. 


267 


HIGHWAY  CONSTRUCTION 


(2)  On  solid,  unyielding  surfaces  it  is  independent  of  the  width 
of  the  tire,  but  on  compressible  surfaces  the  resistance  decreases  as 
the  width  of  the  tire  increases  (but  there  is  no  material  advantage 
gained  in  making  a  tire  more  than  4  inches  wide). 

(3)  It  is  independent  of  the  speed. 

(4)  On  rough,  irregular  surfaces,  which  give  rise  to  constant 
concussion,  it  increases  with  the  speed. 

The  following  table  shows  the  relative  resistance  to  traction  of 
various  surfaces: 

TABLE  1. 
Resistance  to  Traction  on  Different  Road  Surfaces. 


Traction  Resistance. 

Pounds  per  ton. 

In  terms  of  load. 

Earth  road  —  ordinary  condition  
Gravel 

50  to  200 
50  to  100 
100  to  200 
30  to  100 
30  to    50 
15  to    40 

A    toTV 
•    rir   to  A 

A  toTV 

&   to  A 

A  to^ 

T*T  to  Ja 

Sand 

Macadam  

Steel  Wheelway  

These  coefficients  refer  to  the  power  required  to  keep  the  load 
in  motion.  It  requires  from  two  to  six  or  eight  times  as  much  force 
to  start  a  load  as  it  does  to  keep  it  in  motion,  at  two  or  three  miles 
per  hour.  The  extra  force  required  to  start  a  load  is  due  in  part 
to  the  fact  that  during  the  stop  the  wheel  may  settle  into  the  road 
surface,  in  part  to  the  fact  that  the  axle  friction  at  starting  is  greater 
than  after  motion  has  begun,  and  further  in  part  to  the  fact  that 
energy  is  consumed  in  accelerating  the  load. 

Resistance  to  Rolling.  This  resistance  is  caused  (1)  by  the 
wheel  penetrating  or  sinking  below  the  surface  of  the  road,  leaving 
a  track  or  rut  behind  it.  It  is  equal  to  the  product  of  the  load  mul- 
tiplied by  one-third  of  the  semi-chord  of  the  submerged  arc  of  the 
wheel;  and  (2)  by  the  wheel  striking  or  colliding  with  loose  or  pro- 
jecting stones,  which  give  a  sudden  check  to  the  horses,  depending 
upon  the  height  of  the  obstacle,  the  momentum  destroyed  being 
oftentimes  considerable. 

The  rolling  resistance  varies  inversely  as  some  function  of  the 


868 


HIGHWAY  CONSTRUCTION 


diameter  of  the  wheel,  as  the  larger  the  wheel  the  less  force  required 
to  lift  it  over  the  obstruction  or  to  roll  it  up  the  inclination  due  to  the 
indentation  of  the  surface. 

The  powrer  required  to  draw  a  wheel  over  a  stone  or  any  ob- 
stacle, such  as  S  in  Fig.  1,  may  be  thus  calculated.  Let  P  represent 
the  powrer  sought,  or  that  which  would  just  balance  the  weight  on 

the  point  of  the  stone,  and  the 
slightest  increase  of  which 
would  draw  it  over.  This 
power  acts  in  the  direction 
C  P  with  the  leverage  of  B  C 
or  D  E.  Gravity,  represented 
by  W,  resists  in  the  direction 
C  B  with  the  leverage  B  D. 
The  equation  of  equilibrium 


s 
Fig.  1. 


will  be  P  X  C  B  =  W  X  B  D,  whence 


=  \\ 


7BD 
CB 


v  CD2-BC2 
CD  -AD 


Let  the  radius  of  the  wheel  =  C  D  -  26  inches,  and  the  height 
of  the  obstacle  =  A  B  =  4  inches.  Let  the  weight  W  =  500  pounds, 
of  which  200  pounds  may  be  the  weight  of  the  wheel  and  300  pounds 
the  load  on  the  axle.  The  formula  then  becomes 


P-500 


676  -  484 
26-4 


500 


13.85 


-  =  314.7  pounds. 


The  pressure  at  the  point  D  is  compounded  of  the  weight  and 
the  power,  and  equals 

fD  9fi 

W^  =  500  Xg  =  591  pounds, 

and  therefore  acts  with  this  great  effect  to  destroy  the  road  in  its 
collision  with  the  stone,  in  addition  there  is  to  be  considered  the 
effect  of  the  blow  given  by  the  wheel  in  descending  from  it.  For 
minute  accuracy  the  non-horizontal  direction  of  the  draught  and 
the  thickness  of  the  axle  should  be  taken  into  account.  The  power 
required  is  lessened  by  proper  springs  to  vehicles,  by  enlarged  wheels, 
and  by  making  the  line  of  draught  ascending. 


HIGHWAY  CONSTRUCTION 


The  mechanical  advantage  of  the  wheel  in  surmounting  an 
obstacle  may  be  computed  from  the  principle  of  the  lever. 

Let  the  wheel,  Fig.  2,  touch  the  horizontal  line  of  traction  in 
the  point  A  and  meet  a  protuberance  B  D.     Suppose  the  line  of 
draught  C  P  to  be  parallel  to  A  B.     Join  C  D  and  draw  the  perpen- 
diculars DE  and  D  F.      We 
may  suppose  the  power  to  be 
applied  at  E  and  the  weight  at 
F,  and  the  action  is  then  the 
same  as  the  bent  lever  E  D  F 
turning  round  the  fulcrum  at 
D.    HencePrW  ::FD  :DE. 
But  FD  :DE  ::tanFCD:l, 
A~     ^B  and     tan     F  C  D   =    tan    2 

(DAB);    therefore    P   =   W 

tan  2  (DAB).  Now  it  is  obvious  that  the  angle  DAB  increases 
as  the  radius  of  the  circle  diminishes;  and  therefore,  the  weight  W 
being  constant,  the  power  required  to  overcome  an  obstacle  of  given 
height  is  diminished  when  the  diameter  is  increased.  Large  wheels 
are  therefore  the  best  adapted  for  surmounting  inequalities  of  the 
road. 

There  are,  however,  circumstances  which  provide  limits  to  the 
height  of  the  wheels  of  vehicles.  If  the  radius  AC  exceeds  the 
height  of  that  part  of  the  horse  to  which  the  traces  are  attached, 
the  line  of  traction  C  P  will  be  inclined  to  the  horse,  and  part  of  the 
power  will  be  exerted  in  pressing  the  wheel  against  the  ground.  The 
best  average  size  of  wheels  is  considered  to  be  about  6  feet  in  diameter. 
Wheels  of  large  diameter  do  less  damage  to  a  road  than  small 
ones,  and  cause  less  draught  for  the  horses. 

With  the  same  load,  a  two-wheeled  cart  does  far  more  damage 
than  one  with  four  wheels,  and  this  because  of  their  sudden  and 
irregular  twisting  motion  in  the  trackway. 

Grade  Resistance  is  due  to  the  action  of  gravity,  and  is  the 
same  on  good  and  bad  roads.  On  level  roads  its  effect  is  immaterial, 
as  it  acts  in  a  direction  perpendicular  to  the  plane  of  the  horizon,  and 
neither  accelerates  nor  retards  motion.  On  inclined  roads  it  offers 
considerable  resistance,  proportional  to  the  steepness  of  the  incline. 


270 


HIGHWAY  CONSTRUCTION 


The  resistance  due  to  gravity  on  any  incline  in  pounds  per  ton 

2000 

is  equal  to  — » T— 

rate  ot  grade 

The  following  table  shows  the  resistance  due  to  gravity  on  dif- 
ferent grades. 

TABLE  2. 
Resistance  Due  to  Gravity  on  Different  Inclinations. 

Grade  1  in 20    30    40    50  60  70  80  90  100  200  300  400 

Rise  in  feet  per  mile  ...  264  176  132  105  88  75  66  58  52  26  17  13 
Resistance  in  Ib.  per  ton  .11274*  56  4538322825  22  11 J  7£  5* 
The  additional  resistance  caused  by  inclines  may  be  investigated 
in  the  following  manner:  Suppose  the  whole  weight  to  be  borne  on 
one  pair  of  wheels,  and  that  the  tractive  force  is  applied  in  a  direction 
parallel  to  the  surface  of  the  road. 

Let  A  B  in  Fig.  3  represent  a  portion  of  the  inclined  road,  C 
being  a  vehicle  just  sustained  in  its  position  by  a  force  acting  in  the 
direction  CD.  It  is  evident  that  the  vehicle  is  kept  in  its  position 
by  three  forces;  namely,  by  its  own  weight  W  acting  in  the  vertical 
direction  C  F,  by  the  force  F  applied  in  the  direction  C  D  parallel 
to  the  surface  of  the  road,  and  by  the  pressure  P  which  the  vehicle 
exerts  against  the  surface  of  the  road  acting  in  the  direction  C  E 

perpendicular  to  same.  To 
determine  the  relative  magni- 
tude of  these  three  forces, 
draw  a  horizontal  line  A  G 
and  the  vertical  one  B  G; 
then,  since  the  two  lines  C  F 
and  B  G  are  parallel  and 
are  both  cut  by  the  line  A  B, 

Pig.  3.  they     must     make     the    two 

angles     C  F  E    and     A  B  G 

equal ;  also  the  two  angles  C  E  F  and  A  G  B  are  equal ;  therefore,  the 
remaining  angles  F  C  E  and  BAG  are  equal,  and  the  two  triangles 
C  F  E  and  A  B  G  are  similar.  And  as  the  three  sides  of  the  former 
are  proportional  to  the  three  forces  by  which  the  vehicle  is  sustained, 
so  also  are  the  three  sides  of  the  latter;  namely,  AB  or  the  length 
of  the  road  is  proportional  to  W,  or  the  weight  of  the  vehicle;  B  G, 


271 


6  HIGHWAY  COXSTKUCTION 

or  the  vertical  rise  in  the  same,  to  F,  or  the  force  required  to  sustain 
the  vehicle  on  the  incline;  and  A  G,  or  the  horizontal  distance  in 
which  the  rise  occurs,  to  P,  or  the  force  writh  which  the  vehicle  presses 
upon  the  surface  of  the  road.  Therefore, 

W  :  A  B  :  :  F  :  G  B, 
and 

W  :AB  :  :P  :  A  G. 

If  to  A  G  such  a  value  be  assigned  that  the  vertical  rise  of  the 
road  is  exactly  one  foot,  then 

p=W  _W_     =  W-sin4 

AB      i/AG2+l 

and 

_      W-AG        W-AG 

P  =  —        —  =     .  =  W  •  cos  A, 

AB          l/AG-'+l 

in  which  A  is  the  angle  BAG. 

To  find  the  force  requisite  to  sustain  a  vehicle  upon  an  inclined 
road  (the  effects  of  friction  being  neglected),  divide  the  weight  of  the 
vehicle  and  its  load  by  the  inclined  length  of  the  road,  the  vertical 
rise  of  which  is  one  foot,  and  the  quotient  is  the  force  required. 

To  find  the  pressure  of  a  vehicle  against  the  surface  of  an  inclined 
road,  multiply  the  weight  of  the  loaded  vehicle  by  the  horizontal 
length  of  the  road',  and  divide  the  product  by  the  inclined  length  of 
the  same;  the  quotient  is  the  pressure  required. 

The  force  with  which  a  vehicle  presses  upon  an  inclined  road 
is  always  less  than  its  actual  weight;  the  difference  is  so  small  that, 
unless  the  inclination  is  very  steep,  it  may  be  taken  equal  to  the 
weight  of  the  loaded  vehicle. 

To  find  the  resistance  to  traction  in  passing  up  or  down  an 
incline,  ascertain  the  resistance  on  a -level  road  having  the  same  surface 
as  the  incline,  to  which  add,  if  the  vehicle  ascends,  or  subtract,  if 
it  descends,  the  force  requisite  to  sustain  it  on  the  incline;  the  sum 
or  difference,  as  the  case  may  be,  will  express  the  resistance. 

Tractive  Power  and  Gradients.  The  necessity  for  easy 
grades  is  dependent  upon  the  power  of  the  horse  to  overcome  the 
resistance  to  motion  composed  of  the  four  forces,  friction,  collision, 
gravity,  and  the  resistance  of  the  air. 

All  estimates  on  the  tractive  power  of  horses  must  to  a  certain 


272 


HIGHWAY  CONSTRUCTION 


extent  be  vague,  owing  to  the  different  strengths  and  speeds  of  animals 
of  the  same  kind,  as  well  as  to  the  extent  of  their  training  to  any 
particular  kind  of  work. 

The  draught  or  pull  which  a  good  average  horse,  weighing  1,200 
pounds,  can  exert  on  a  level,  smooth  road  at  a  speed  of  2^  miles  per 
hour  is  100  pounds,  equivalent  to  22,000  foot-pounds  per  minute, 
or  13,200,000  foot-pounds  per  day  of  10  hours. 

The  tractive  power  diminishes  as  the  speed  increases  and,  per- 
haps, within  certain  limits,  say  from  f  to  4  miles  per  hour,  nearly 
in  inverse  proportion  to  it.  Thus  the  average  tractive  force  of  a 
horse,  on  a  level,  and  actually  pulling  for  10  hours,  may  be  assumed 

approximately  as  follows: 

TABLE  3. 
Tractive  Power  of  Horses  at  Different  Velocities. 


Miles  per  hour. 

Tractive 
Force.    Lb. 

Miles  per  hour. 

Tractive 
Force.     Lb. 

3 

333  33 

21 

Ill    11 

1 

250 

2i 

100 

li 

200 

90  91 

1$ 

166  66 

3 

83  33 

142.86 

3J  

71.43 

2 

125 

4 

62  50 

The  work  done  by  a  horse  is  greatest  when  the  velocity  with 
which  he  moves  is  £  of  the  greatest  velocity  with  which  he  can  move 
when  unloaded;  and  the  force  thus  exerted  is  0.45  of  the  utmost 
force  that  he  can  exert  at  a  dead  pull. 

The-  traction  power  of  a  horse  may  be  increased  in  about  the 
same  proportion  as  the  time  is  diminished,  so  that  when  working 
from  5  to  10  hours,  on  a  level,  it  will  be  about  as  shown  in  the  following 

table: 

TABLE  4. 

Hours  per  day  Traction  (pounds)   Hours  per  day  Traction  (pounds) 


10     .....  .....         100  7     .......... 

9     ..........         111^  6     .......... 

8     ..........         125  5     .......... 

The  tractive  power  of  teams  is  about  as  follows 

1  horse     ..............  =1 

2  horses  ..............  0  .  95  X  2  =  1  .  90 

3  "       ........  ......  0.85  X  3  -  2.55 

4  "  0.80X  4-3.20 


146| 
166J 
200 


273 


HIGHWAY  CONSTRUCTION 


Loss  of  Tractive  Power  on  Inclines.  In  ascending  in- 
clines a  horse's  power  diminishes  rapidly;  a  large  portion  of  his 
strength  is  expended  in  overcoming  the  resistance  of  gravity  due  to 
his  own  weight  and  that  of  the  load.  Table  5  shows  that  as  the 
steepness  of  the  grade  increases  the  efficiency  of  both  the  horse  and 
the  road  surface  diminishes;  that  the  more  of  the  horse's  energy  is 
expended  in  overcoming  gravity  the  less  remains  to  overcome  the 
surface  resistance. 

TABLE  5. 

Effects  of  Grades  Upon  the  Load  a  Horse  can  Draw  on  Different 
Pavements. 


Grade. 

Earth. 

Broken  Stone. 

Stone  Blocks. 

Asphalt. 

Level 

1.00 

1.00 

1.00 

1.00 

1  :  100 

.80 

.66 

.72 

.41 

2  :  100 

.66 

.50 

.55 

.25 

3  :  100 

.55 

.40 

.44 

.18 

4  :  100 

.47 

.33 

.36 

.13 

5  :  100 

.41 

.29 

.30 

.10 

10  :  100 

.26 

.16 

.14 

.04 

15  :  100 

.10 

.05 

.07 

20  :  100 

.04 

.03 

Table  6  shows  the  gross  load  which  an  average  horse,  weighing 
1,200  pounds,  can  draw  on  different  kinds  of  road  surfaces,  on  a 
level  and  on  grades  rising  five  and  ten  feet  per  one  hundred  feet. 

TABLE  6. 


Description  of  Surface. 

Level. 

5  per  cent 
grade. 

10  per  cent 
grade. 

\sphalt 

13  216 

Broken  stone  (best  condition) 

6  700 

1  840 

1  060 

"      (slightly  muddy)  

4,700 

1,500 

1,000 

'           "      (ruts  and  mud) 

3  000 

1  390 

890 

"      (very  bad  condition)   .  . 

1,840 

1,040 

740 

Earth               (best  condition)  

3,600 

1,500 

930 

(average  condition)  .... 

1,400 

900 

660 

(moist  but  not  muddy). 

1,100 

780 

600 

Stone-block  pavement  (dry  and  clean) 

8,300 

1,920 

1,090 

"          (muddy)  

6,250 

1,800 

1,040 

Sand  (wet)  

1,500 

675 

390 

"      (dry)  

1,087 

445 

217 

The  decrease  in  the  load  which  a  horse  can  draw  upon  an  incline 
is  not  due  alone  to  gravity;  it  varies  with  the  amount  of  foothold 


274 


HIGHWAY  CONSTRUCTION 


afforded  by  the  road  surface.  The  tangent  of  the  angle  of  inclination 
should  not  be  greater  than  the  coefficient  of  tractional  resistance; 
therefore  it  is  evident  that  the  smoother  the  road  surface,  the  easier 
should  be  the  grade.  The  smoother  the  surface  the  less  the  foothold, 
and  consequently  the  load. 

The  loss  of  tractive  power  on  inclines  is  greater  than  any  inves- 
tigation will  show;  for,  besides  the  increase  of  draught  caused  by 
gravity,  the  power  of  the  horse  is  much  diminished  by  fatigue  upon 
a  long  ascent,  and  even  in  greater  ratio  than  man,  owing  to  its  anatom- 
ical formation  and  great  weight.  Though  a  horse  on  a  level  is  as 
strong  as  five  men,  on  a  grade  of  15  per  cent,  it  is  less  strong  than 
three;  for  three  men  carrying  each  100  pounds  will  ascend  such  a 
grade  faster  and  with  less  fatigue  than  a  horse  with  300  pounds. 

A  horse  can  exert  for  a  short  time  twice  the  average  tractive 
pull  which  he  can  exert  continuously  throughout  the  day's  work; 
hence,  so  long  as  the  resistance  on  the  incline  is  not  more  than  double 
the  resistance  on  the  level,  the  horse  will  be  able  to  take  up  the  full 
load  which  he  is  capable  of  drawing. 

Steep  grades  are  thus  seen  to  be  objectionable,  and  particularly 
so  when  a  single  one  occurs  on  an  otherwise  comparatively  level  road, 
in  which  case  the  load  carried  over  the  less  inclined  portions  must 
be  reduced  to  what  can  be  hauled  up  the  steeper  portion. 

The  bad  effects  of  steep  grades  are  especially  felt  in  winter, 
when  ice  covers  the  roads,  for  the  slippery  condition  of  the  surface 
causes  danger  in  descending,  as  well  as  increased  labor  in  ascending; 
the  water  of  rains  also  runs  down  the  road  and  gulleys  it  out,  destroy- 
ing its  surface,  thus  causing  a  constant  expense  for  repairs.  The 
inclined  portions  are  subject  to  greater  wear  from  horses  ascending, 
thus  requiring  thicker  covering  than  the  more  level  portions,  and 
hence  increasing  the  cost  of  construction. 

It  will  rarely  be  possible,  except  in  a  flat  or  comparatively  level 
country,  to  combine"  easy  grades  with  the  best  and  most  direct  route. 
These  two  requirements  will  often  conflict.  In  such  a  case,  increase 
the  length.  The  proportion  of  this  increase  will  depend  upon  the 
friction  of  the  covering  adopted.  But  no  general  rule  can  be  given 
to  meet  all  cases  as  respects  the  length  which  may  thus  be  added, 
for  the  comparative  time  occupied  in  making  the  journey  forms  an 


275 


10 


HIGHWAY  CONSTRUCTION 


important  element  in  any  case  which  arises  for  settlement.  Disre- 
garding time,  the  horizontal  length  of  a  road  may  be  increased  to 
avoid  a  5  per  cent  grade,  seventy  times  the  height. 

Table  7  shows,  for  most  practical  purposes,  the  force  required 
to  draw  loaded  vehicles  over  inclined  roads.  The  first  column  ex- 
presses the  rate  of  inclination;  the  second,  the  pressure  on  the  plane 
in  pounds  per  ton;  the  third,  the  tendency  down  the  plane  (or  force 
required  to  overcome  the  effect  of  gravity)  in  pounds  per  ton;  the 
fourth,  the  force  required  to  haul  one  ton  up  the  incline;  the  fifth,  the 
length  of  level  road  which  would  be  equivalent  to  a  mile  in  length  of 
the  inclined  road — that  is,  the  length  which  would  require  the  same 
motive  power  to  be  expended  in  drawing  the  load  over  it,  as  would 
be  necessary  to  draw  over  a  mile  of  the  inclined  road',  the  sixth,  the 
maximum  load  which  an  average  horse  weighing  1,200  pounds  can 
draw  over  such  inclines,  the  friction  of  the  surface  being  taken  at 
-fo  of  the  load  drawn. 

TABLE  7. 


Rate  of  grade. 
Feet  per  100 
feet. 

Pressure   on 
the  plane  in 
Ib.  per  ton. 

Tendency 
down  the 
plane  in  Ib. 
per  ton. 

Power  in  Ib. 
required    to 
haul  one  ton 
up  the  plane. 

Equivalent 
length  of  level 
road.    Miles. 

Maximum 
load  in  Ib. 
which  a  horse 
can  haul. 

0.0 

2240 

.00 

45.00              1.000 

6270 

0.25 

2240 

5.60 

50.60             1.121 

5376 

0.50 

2240 

11.20 

56.20 

1.242 

4973 

0.75 

2240 

16.80 

61.80 

1.373 

4490 

1. 

2240 

22.40 

67.40 

1.500 

4145 

1.25 

*2240 

28.00 

73.00 

1.622 

3830 

1  .  50 

2240 

33.60 

78.60 

1.746 

3584 

1.75 

2240 

39.20 

84.20 

1.871 

3290 

2 

2240 

45.00 

90.00 

2.000 

3114 

2  25 

2240 

50.40 

95.4'0 

2.120 

2935 

2^50 

2240 

56.00 

101.00 

2.244 

2725 

2.75 

2240 

61.33 

106.33 

2.363 

2620 

3 

2239 

67.20 

112.20 

2.484 

2486 

4 

2238 

89.20 

134.20 

2.982 

2083 

5 

2237 

112.00 

157.00 

3.444 

1800 

6 

2233 

134.40 

179.40 

3.986 

1568 

7 

2232 

156.80 

201.80 

4.844 

1367 

8 

2232 

179.20 

224  .  20 

4.982 

1235 

9 

2231 

201.60 

246.60 

5.840 

1125 

10 

2229 

224.00 

269.00 

5.977 

1030 

*  Near  enough  for  practice;  actually  2239.888. 

Pressure  on  the  plane  =  weight  x  nat  cos  of  angle  of  plane. 

Axle  Friction.      The  resistance  of  the  hub  to  turning  on   the 
axle  is  the  same  as  that  of  a  journal  revolving  in  its  bearing,  and  has 


276 


HIGHWAY  CONSTRUCTION  11 

nothing  to  do  with  the  condition  of  the  road  surface.  The  coefficient 
of  journal  friction  varies  with  the  material  of  the  journal  and  its 
bearing,  and  with  the  lubricant.  It  is  nearly  independent  of  the 
velocity,  and  seems  to  vary  about  inversely  as  the  square  root  of  the 
pressure.  For  light  carriages  when  loaded,  the  coefficient  of  friction 
is  about  0.020  of  the  weight  on  the  axle;  for  the  ordinary  thimble- 
skein  wagon  when  loaded,  it  is  about  0.012.  These  coefficients  are 
for  good  lubrication;  if  the  lubrication  is  deficient,  the  axle  friction 
is  two  to  six  times  as  much  as  above. 

The  traction  power  required  to  overcome  the  above  axle  friction 
for  carriages  of  the  usual  proportions  is  about  3  to  3^  Ib.  per  ton  of 
the  weight  on  the  axle;  and  for  truck  wagons,  which  have  medium 
sized  wheels  and  axles,  is  about  3  j.  to  4^  Ib.  per  ton. 

Resistance  of  the  Air.  The  resistance  arising  from  the 
force  of  the  wind  will  vary  with  the  velocity  of  the  wind,  with  the 
velocity  of  the  vehicle,  with  the  area  of  the  surface  acted  upon,  and 
also  with  the  angle  of  incidence  of  direction  of  the  wind  with  the 
plane  of  the  surface. 

The  following  table  gives  the  force  per  square  foot  for  various 
velocities: 

TABLE  8. 


Velocity  of  wind  in  miles 
per  hour. 

Force  in  Ibs.  per  sq.  ft. 

Description. 

15                                          1.107 

Pleasant  Breeze 

20 
25 

1.968\ 
3.075/ 

Brisk  Gale 

30 
35 

4.428\ 
6.027J 

High  Wind 

40 
45 

7.872) 
9.963\ 

Very  High  Wind 

50                                    12.300                            Storm 

Effect  of  Springs  on  Vehicles.  Experiments  have  shown 
that  vehicles  mounted  on  springs  materially  decrease  the  resistance  to 
traction,  and  diminish  the  wear  of  the  road,  especially  at  speeds 
beyond  a  walking  pace.  Going  at  a  trot,  they  were  found  not  to 
cause  more  wear  than  vehicles  without  springs  at  a.  walk,  all  other 
conditions  being  similar.  Vehicles  with  springs  improperly  fixed 
cause  considerable  concussion,  which  in  turn  destroys  the  road 
covering. 


277 


12  HIGHWAY  CONSTRUCTION 

LOCATION  OF  COUNTRY  ROADS. 

The  considerations  governing  the  location  of  country  roads  are 
dependent  upon  the  commercial  condition  of  the  country  to  be 
traversed.  In  old  and  long-inhabited  sections  the  controlling  ele- 
ments will  be  the  character  of  the  traffic  to  be  accommodated.  In 
such  a  section,  the  route  is  generally  predetermined,  and  therefore 
there  is  less  liberty  of  a  choice  and  selection  than  in  a  new  and  sparsely 
settled  district,  where  the  object  is  to  establish  the  easiest,  shortest, 
and  most  economical  line  of  intercommunication  according  to  the 
physical  character  of  the  ground. 

Whichever  of  these  two  cases  may  have  to  be'dealt  with,  the  same 
principle  governs  the  engineer,  namely,  to  so  lay  out  the  road  as  to 
effect  the  conveyance  of  the  traffic  with  the  least  expenditure  of 
motive  power  consistent  with  economy  of  construction  and  main- 
tenance. 

Economy  of  motive  power  is  promoted  by  easy  grades,  by  the 
avoidance  of  all  unnecessary  ascents  and  descents,  and  by  a  direct 
line;  but  directness  must  be  sacrificed  to  secure  easy  grades  and  to 
avoid  expensive  construction. 

Reconnoissance.  The  selection  of  the  best  route  demands 
much  care  and  consideration  on  the  part  of  the  engineer.  To  obtain 
the  requisite  data  upon  which  to  form  his  judgment,  he  must  make 
a  personal  reconnoissance  of  the  district.  This  requires  that  the 
proposed  route  be  either  ridden  or  walked  over  and  a  careful  examina- 
tion made  of  the  principal  physical  contours  and  natural  features  of 
the  district.  The  amount  of  care  demanded  and  the  difficulties 
attending  the  operations  will  altogether  depend  upon  the  character 
of  the  country. 

The  immediate  object  of  the  reconnoissance  is  to  select  one  or 
more  trial  lines,  from  which  the  final  route  may  be  ultimately  deter- 
mined. 

When  there  are  no  maps  of  the  section  traversed,  or  when  those 
which  can  be  procured  are  indefinite  or  inaccurate,  the  work  of 
reconnoitering  will  be  much  increased. 

In  making  a  reconnoissance  there  are  several  points  which,  if 
carefully  attended  to,  will  very  considerably  lessen  the  labor  and 
time  otherwise  required.  Lines  which  would  run  along  the  imme- 


278 


HIGHWAY  CONSTRUCTION  13 

diate  bank  of  a  large  stream  must  of  necessity  intersect  all  the  tribu- 
taries confluent  on  that  bank,  thereby  demanding  a  corresponding 
number  of  bridges.  Those,  again,  which  are  situated  along  the 
slopes  of  hills  are  more  liable  in  rainy  weather  to  suffer  from  washing 
away  of  the  earthwork  and  sliding  of  the  embankments;  the  others 
which  are  placed  in  valleys  or  elevated  plateaux,  when  the  line  crosses 
the  ridges  dividing  the  principal  water  courses  will  have  steep  ascents 
and  descents. 

In  making  an  examination  of  a  tract  of  country,  the  first  point 
to  attract  notice  is  the  unevenness  or  undulations  of  its  surface,  which 
appears  to  be  entirely  without  system,  order,  or  arrangement;  but 
upon  closer  examination  it  will  be  perceived  that  one  general  prin- 
ciple of  configuration  obtains  even  in  the  most  irregular  countries. 
The  country'  is  intersected  in  various  directions  by  main  water  courses 
or  rivers,  which  increase  in  size  as  they  approach  the  point  of  their 
discharge.  Towards  these  main  rivers  lesser  rivers  approach  on 
both  sides,  running  right  and  left  through  the  country,  and  into  these, 
again,  enter  still  smaller  streams  and  brooks.  The  streams  thus 
divide  the  hills  into  branches  or  spurs  having  approximately  the  same 
direction  as  themselves,  and  the  ground  falls  in  every  direction  from 
the  main  chain  of  hills  towards  the  water  courses,  forming  ridges 
more  or  less  elevated.  . 

The  main  ridge  is  cut  down  at  the  heads  of  the  streams  into 
depressions  called  gaps  or  passes;  the  more  elevated  points  are  called 
peaks.  The  water  which  has  fallen  upon  these  peaks  is  the  origin 
of  the  streams  which  have  hollowed  out  the  valleys.  Furthermore, 
the  ground  falls  in  every  direction  towards  the  natural  water  courses, 
forming  ridges  more  or  less  elevated  running  between  them  and 
separating  from  each  other  the  districts  drained  by  the  streams. 

The  natural  water  courses  mark  not  only  the  lowest  lines,  but 
the  lines  of  the  greatest  longitudinal  slope  in  the  valleys  through  which 
they  flow. 

The  direction  and  position  of  the  principal  streams  give  also 
the  direction  and  approximate  position  of  the  high  ground  or  ridges 
which  lie  between  them. 

The  positions  of  the  tributaries  to  the  larger  stream  generally 
indicate  the  points  of  greatest  depression  in  the  summits  of  the  ridges, 


279 


U  HIGHWAY  CONSTRUCTION 


Fig.  4.    Contour  Lines. 


HIGHWAY  CONSTRUCTION  15 

and  therefore  the  points  at  which  lateral  communication  across  the 
high  ground  separating  contiguous  valleys  can  be  most  readily  made. 

The  instruments  employed  in  reconnoitering,  are :  The  compass, 
for  ascertaining  the  direction;  the  aneroid  barometer,  to  fix  the  ap- 
proximate elevation  of  summits,  etc. ;  and  the  hand  level,  to  ascertain 
the  elevation  of  neighboring  points.  If  a  vehicle  can  be  used,  an 
odometer  may  be  added,  but  distances  can  usually  be  guessed  or 
ascertained  by  time  estimates  or  otherwise,  closely  enough  for  pre- 
liminary purposes.  The  best  maps  obtainable  and  traveling  com- 
panions who  possess  a  local  knowledge  of  the  country,  together  with 
the  above  outfit  is  all  that  will  be  necessary  for  the  first  inspection. 

The  reconnoissance  being  completed,  instrumental  surveys  of 
the  routes  deemed  most  advantageous  should  be  made.  When  the 
several  lines  are  plotted  to  the  same  scale,  a  good  map  can  be  pre- 
pared from  which  the  exact  location  of  the  road  can  be  determined. 

In  making  the  preliminary  surveys  the  topographical  features 
should  be  noted  for  a  convenient  distance  to  the  right  and  the  left  of 
the  line,  and  all  prominent  points  located  by  compass  bearings.  The 
following  data  should  also  be  obtained:  the  importance,  magnitude, 
and  direction  of  all  streams  and  roads  crossed;  the  character  of  the 
material  to  be  excavated  or  available  for  embankments,  the  position 
of  quarries  and  gravel  pits,  and  the  modes  of  access  thereto;  and  all 
other  information  that  may  effect  a  selection. 

Topography.  There  are  various  methods  of  delineating  upon 
paper  the  irregularities  of  the  surface  of  the  ground.  The  method 
of  most  utility  to  the  engineer  is  that  by  means  of  "contour  lines." 
These  are  fine  lines  traced  through  the  points  of  equal  level  over  the 
surface  surveyed,  and  denote  that  the  level  of  the  ground  throughout 
the  whole  of  their  course  is  identical;  that  is  to  say,  that  every  part 
of  the  ground  over  which  the  line  passes  is  at  a  certain  height  above 
a  known  fixed  point  termed  the  datum,  this  height  being  indicated 
by  the  figures  written  against  the  line. 

The  intervals  between  the  lines  vertically  are  equal  and  may 
be  1,  3,  5,  10  or  more  feet  apart;  where  the  surface  is  very  steep  they 
lie  close  together.  These  lines  by  their  greater  or  less  distance  apart 
have  the  effect  of  shading,  and  make  apparent  to  the  eye,  the 
undulations  and  irregularities  in  the  surface  of  the  country. 


HIGHWAY  CONSTRUCTION 


—  60.00 


1-55.00 


-  54.20 


-  54.4 


-  54.62 


Fig.  4  shows  an  imaginary  tract  of  country,  the  physical  features 
of  which  are  shown  by  contour  lines. 

Map.  The  map  should  show  the 
lengths  and  direction  of  the  different  por- 
tions of  the  line,  the  topography,  rivers, 
water  courses,  roads,  railroads,  and  other 
matters  of  interest,  such  as  town  and 
county  lines,  dividing  lines  between  property, 
timbered  and  cultivated  lands,  etc. 

Any  convenient  scale  may  be  adopted; 
400  feet  to  an  inch  will  be  found  the  most 
useful. 

Memoir.  The  descriptive  memoir 
should  give  with  minuteness  all  information, 
such  as  the  nature  of  the  soil,  character  of 
the  several  excavations  whether  earth  or 
rock,  and  such  particular  features  as  can- 
not be  clearly  shown  upon  the  map  or 
profile. 

Special  information  should  be  given  re- 
garding the  rivers  crossed,  as  to  their  width, 
depth  at  highest  known  flood,  velocity  of 
current,  character  of  banks  and  bottom, 
and  the  angle  of  skew  which  the  course 
makes  with  the  line  of  the  road. 

Levels.  Levels  should  be  taken  along 
the  course  of  each  line,  usually  at  every  100 
feet,  or  at  closer  intervals,  depending  upon 
the  nature  of  the  country. 

In  taking  the  levels,  the  heights  of 
all  existing  roads,  railroads,  rivers,  or 
canals  should  be  noted.  "Bench  marks" 
should  be  established  at  least  every  half 
mile,  that  is,  marks  made  on  any  fixed 
object,  such  as  a  gate  post,  side  of  a  house, 
or,  in  the  absence  of  these,  a  cut  made 
on  a  large  tree.  The  height  and  exact 


—  55.10- 


—  55.00- 


Fig.  5.    Preliminary  Profile 


HIGHWAY  CONSTRUCTION  17 

description  of  each  bench  mark  should  be  recorded  in  the  level  book. 

Cross  Levels.  Wherever  considered  necessary  levels  at  right 
angle  to  the  center  line  should  be  taken.  These  will  be  found  useful 
in  showing  what  effect  a  deviation  to  the  right  or  left  of  the  surveyed 
line  would  have.  Cross  levels  should  be  taken  at  the  intersection  of 
all  roads  and  railroads  to  show  to  what  extent,  if  any,  these  levels 
will  have  to  be  altered  to  suit  the  levels  of  the  proposed  road. 

Profile.  A  profile  is  a  longitudinal  section  of  the  route,  made 
from  the  levels.  Its  horizontal  scale  should  be  the  same  as  that  of 
the  map;  the  vertical  scale  should  be  such  as  will  show  with  distinct- 
ness the  inequalities  of  .the  ground. " 

Fig.  5  shows  the  manner  in  which  a  profile  is  drawn  and  the 
nature  of  the  information  to  be  given  upon  it. 

Bridge  Sites,  The  question  of  choosing  the  site  of  bridges  is 
an  important  one.  If  the  selection  is  not  restricted  to  a  particular 
point,  the  river  should  be  examined  for  a  considerable  distance  above 
and  below  what  would  be  the  most  convenient  point  for  crossing;  and 
if  a  better  site  is  found,  the  line  of  the  road  must  be  made  subordinate 
to  it.  If  several  practicable  crossings  exist,  they  must.be  carefully 
compared  in  order  to  select  the  one  most  advantageous.  The  follow- 
ing are  controlling  conditions:  (1)  Good  character  of  the  river  bed, 
affording  a  firm  foundation.  If  rock  is  present  near  the  surface  of 
the  river  bed,  the  foundation  will  be  easy  of  execution  and  stability 
and  economy  will  be  insured.  (2)  Stability  of  river  banks,  thus 
securing  a  permanent  concentration  of  the  waters  in  the  same  bed. 
(3)  The  axis  of  the  bridge  should  be  at  right  angles  to  the  direction 
of  the  current.  (4)  Bends  in  rivers  are  not  suitable  localities  and 
should  be  avoided  if  possible.  A  straight  reach  above  the  bridge 
should  be  'secured  if  possible. 

Final  Selection.  In  making  the  final  selection  the  following 
principles  should  be  observed  as  far  as  practicable. 

(a)  To  follow  that  route  which  affords  the  easiest  grades.  The 
easiest  grade  for  a  given  road  will  depend  on  the  kind  of  covering 
adopted  for  its  surface. 

(6)  To  connect  the  places  by  the  shortest  and  most  direct  route 
commensurate  with  easy  grades. 

(c)  To  avoid  all  unnecessary  ascents  and  descents.     When  a 


18  HIGHWAY  CONSTRUCTION 

road  is  encumbered  with  useless  ascents,  the  wasteful  expenditure  of 
power  is  considerable. 

(d)  To  give  the  center  line  such  a  position,  with  reference  to 
the  natural  surface  of  the  ground,  that  the  cost  of  construction  shall 
be  reduced  to  the  smallest  possible  amount. 

(e)  To  cross  all  obstacles  (where  structures  are  necessary)  as 
nearly  as  possible  at  right  angles.     The  cost  of  skew  structures 
increases  nearly  as  the  square  of  the  secant  of  the  obliquity. 

(/)  To  cross  ridges  through  the  lowest  pass  which  occurs. 

(</)  To  cross  either  under  or  over  railroads;  for  grade  crossings 
mean  danger  to  every  user  of  the  highway. 

Examples  of  Cases  to  be  Treated.  In  laying  out  the  line 
of  a  road,  there  are  three  cases  which  may  have  to  be  treated,  and 
each  of  these  is  exemplified  in  the  contour  map,  Fig.  4.  First,  the 
two  places  to  be  connected,  as  the  towns  A  and  B  on  the  plan,  may 
be  both  situated  in  the  same  valley,  and  upon  the  same  side  of  it;  that 
is,  they  are  not  separated  from  each  other  by  the  main  stream  which 
drains  the  valley.  This  is  the  simplest  case.  Secondly,  although 
both  in  the  same  valley,  the  two  places  may  be  on  opposite  sides  of 
the  valley,  as  at  A  and  C,  being  separated  by  the  main  river.  Thirdly, 
they  may  be  situated  in  different  valleys,  separated  by  an  intervening 
ridge  of  ground  more  or  less  elevated,  as  at  A  and  D.  In  laying  out 
an  extensive  line  of  road,  it  frequently  happens  -that  all  these  cases 
have  to  be  dealt  with. 

The  most  perfect  road  is  that  of  which  the  course  is  perfectly 
straight  and  the  surface  practically  level;  and,  all  other  things  being 
the  same,  the  best  road  is  that  wrhich  answrers  nearest  to  this  de- 
scription. 

Now,  in  the  first  case,  that  of  the  two  towns  situated  on  the 
same  side  of  the  main  valley,  there  are  two  methods  which  may  be 
pursued  in  forming  a  communication  between  them.  A  road  follow- 
ing the  direct  line  between  them,  shown  by  the  thick  dotted  line  A  B, 
may  be  made,  or  a  line  may  be  adopted  wrhich  will  gradually  and 
equally  incline  from  one  town  to  another,  supposing  them  to  be  at 
different  levels;  or,  if  they  are  on  the  same  level,  the  line  should  keep 
at  that  level  throughout  its  entire  course,  following  all  the  sinuosities 
and  curves  which  the  irregular  formation  of  the  country  may  render 


HIGHWAY  CONSTRUCTION  19 

necessary  for  the  fulfillment  of  these  conditions.  According  to  the 
first  method,  a  level  or  uniformly  inclined  road  might  be  made  from 
one  to  the  other;  this  line  would  cross  all  the  valleys  and  streams 
which  run  down  to  the  main  river,  thus  necessitating  deep  cuttings, 
heavy  embankments,  and  numerous  bridges;  or  these  expensive 
works  might  be  avoided  by  following  the  sinuosities  of  the  valley. 
When  the  sides  of  the  main  valley  are  pierced  by  numerous  ravines 
with  projecting  spurs  and  ridges  intervening,  instead  of  following  the 
sinuosities,  it  will  be  found  better  to  make  a  nearly  straight  line 
cutting  through  the  projecting  points  in  such  a  way  that  the  material 
excavated  should  be  just  sufficient  to  fill  the  hollows. 

Of  all  these,  the  best  is  the  straight  or  uniformly  inclined,  or 
level  road,  although  at  the  same  time  it  is  the  most  expensive.  If 
the  importance  of  the  traffic  passing  between  the  places  is  not  suffi- 
cient to  warrant  so  great  an  outlay,  it  will  become  a  matter  of  consider- 
ation whether  the  course  of  the  road  should  be  kept  straight,  its  surface 
being  made  to  undulate  with  the  natural  face  of  the  country;  or 
whether,'  a  level  or  equally  inclined  line  being  adopted,  the  course 
of  the  road  should  be  made  to  deviate  from  the  direct  line,  and  follow 
the  winding  course  which  such  a  condition  is  supposed  to  necessitate. 

In  the  second  case,  that  of  two  places  situated  on  opposite  sides 
of  the  same  valley,  there  is,  in  like  manner,  the  choice  of  a  perfectly 
straight  Kne  to  connect  them,  wThich  would  probably  require  a  big 
embankment  if  the  road  was  kept  level,  or  steep  inclines  if  it  followed 
the  surface  of  the  country;  or  by  winding  the  road,  it  may  be  carried 
across  the  valley  at  a  higher  point,  where,  if  the  level  road  be  taken, 
the  embankment  would  not  be  so  high,  or,  if  kept  on  the  surface, 
the  inclination  would  be  reduced. 

In  the  third  case,  there  is,  in  like  manner,  the  alternative  of 
carrying  the  road  across  the  intervening  ridge  in  a  perfectly  straight 
line,  or  of  deviating  it  to  the  right  and  left,  and  crossing  the  ridge 
at  a  point  where  the  elevation  is  less. 

The  proper  determination  of  the  question  which  of  these  courses 
is  the  best  under  certain  circumstances  involves  a  consideration  of 
the  comparative  advantages  and  disadvantages  of  inclines  and 
curves.  What  additional  increase  in  the  length  of  a  road  would  be 
equivalent  to  a  given  inclined  plane  upon  it;  or  conversely,  what 


20  HIGHWAY  CONSTRUCTION 


inclination  might  be  given  to  a  road  as  an  equivalent  to  a  given  de- 
crease in  its  length  ?  To  satisfy  this  question,  the  comparative  force 
required  to  draw  different  vehicles  with  given  loads  must  be  known, 
both  upon  level  and  variously  inclined  roads. 

The  route  which  will  give  the  most  general  satisfaction  consists 
in  following  the  valleys  as  much  as  possible  and  rising  afterward  by 
gentle  grades.  This  course  traverses  the  cultivated  lands,  regions 
studded  with  farmhouses  and  factories.  The  value  of  such  a  line 
is  much  more  considerable  than  that  of  a  route  by  the  ridges.  The 
water  courses  which  flow  down  to  the  main  valley  are,  it  is  true, 
crossed  where  they  are  the  largest  and  require  works  of  large  dimen- 
sions, but  also  they  are  fewer  in  number. 

Intermediate  Towns.  Suppose  that  it  is  desired  to  form  a 
road  between  two  distant  towns,  A  and  B,  Fig.  6,  and  let  us  for  the 
present  neglect  altogether  the  consideration  of  the  physical  features 
of  the  intervening  country,  assuming  that  it  is  equally  favorable 
whichever  line  we  select.  Now  at  first  sight,  it  would  appear  that 
under  such  circumstances  a  perfectly  straight  line  drawn  from  one 

town  to  the  other  would  be 
the  best  that  could  be  chos- 
en.    On  more  careful  exam- 
NN  ination  however,  of  the  lo- 

Ns  cality,    we    may   find    that 

XXN          there   is  a   third    town,   C, 


B       situated    somewhat  on  one 
side    of    the    straight    line 

which  we  have  drawn  from  A  to  B  ;  and  although  our  primary  object 
is  to  connect  only  the  two  latter,  that  it  would  nevertheless  be  of 
considerable  service  if  the  whole  of  the  three  towns  were  put  into 
mutual  connection  with  each  other. 

This  may  be  effected  in  three  different  ways,  any  one  of  which 
might,  under  the  circumstances,  be  the  best.  In  the  first  place,  we 
might,  as  originally  suggested,  form  a  straight  road  from  A  to  B, 
and  in  a  similar  manner  two  other  straight  roads  from  A  to  C,  and 
from  B  to  C,  and  this  would  be  the  most  perfect  way  of  effecting  the 
object  in  view  the  distance  between  any  of  the  two  towns  being 
reduced  to  the  least  possible.  It  would,  however,  be  attended  with 


II 

3  o 


HIGHWAY  CONSTRUCTION  21 

considerable  expense,  and  it  would  be  requisite  to  construct  a  much 
greater  length  of  road  than  according  to  the  second  plan,  which  would 
be  to  form,  as  before,  a  straight  road  from  A  to  B,  and  from  C  to  con- 
struct a  road  which  should  join  the  former  at  a  point  D,  so  as  to  be  per- 
pendicular to  it.  The  traffic  between  A  or  B  and  C  would  proceed  to 
the  point  D  and  then  turn  off  to  C.  With  this  arrangement,  white 
the  length  of  the  roads  would  be  very  materially  decreased,  only  a 
slight  increase  would  be  occasioned  in  the  distance  between  C  and 
the  other  two  towns.  The  third  method  would  be  to  form  only  the 
two  roads  A  C  and  C  B,  in  which  case  the  distance  between  A  and  B 
would  be  somewhat  increased,  while  that  between  A  C  or  B  and  C 
would  be  diminished,  and  the  total  length  of  road  to  be  constructed 
would  also  be  lessened. 

As  a  general  rule  it  may  be  taken  that  the  last  of  these  methods 
is  the  best  and  most  convenient  for  the  public;  that  is  to  say,  that 
if  the  physical  character  of  the  country  does  not  determine  the  course 
of  the  road,  it  will  generally  be  found  best  not  to  adopt  a  perfectly 
straight  line,  but  to  vary  the  line  so  as  to  pass  through  all  the  prin- 
cipal towns  near  its  general  course. 

flountain  Roads.  The  location  of  roads  in  mountainous 
countries  presents  greater  difficulties  than  in  an  ordinary  undulating 
country;  the  same  latitude  in  adopting  undulating  grades  and  choice 
of  position  is  not  permissible,  for  the  maximum  must  be  kept  before 
the  eye  perpetually.  A  mountain  road  has  to  be  constructed  on  the 
maximum  grade  or  at  grades  closely  approximating  it,  and  but  one 
fixed  point  can  be  obtained  before  commencing  the  survey,  antl  that 
is  the  lowest  pass  in  the  mountain  range;  from  this  point  the  survey 
must  be  commenced.  The  reason  for  this  is  that  the  lower  slopes 
of  the  mountain  are  flatter  than  those  at  their  summit;  they  cover  a 
larger  area,  and  merge  into  the  valley  in  diverse  undulations.  So 
that  a  road  at  a  foot  of  a  mountain  may  be  carried  at  will  in  the 
desired  direction  by  more  than  one  route,  while  at  the  top  of  a  moun- 
tain range  any  deviation  from  the  lowest  pass  involves  increased 
length  of  line.  The  engineer  having  less  command  of  the  ground, 
owing  to  the  reduced  area  he  has  to  deal  with  and  the  greater  abrupt- 
ness of  the  slopes,  is  liable  to  be  frustrated  in  his  attempt  to  get  his 
line  carried  in  the  desired  direction. 


287 


22  HIGHWAY  CONSTRUCTION 

It  is  a  common  practice  to  run  a  mountain  survey  up  hill,  but 
this  should  be  avoided.  Whenever  an  acute-angled  zigzag  is  met 
with  on  a  mountain  road  near  the  summit,  the  inference  to  be  drawn 
is  that  the  line  being  carried  up  hill  on  reaching  the  summit  was 
too  low  and  the  zigzag  wras  necessary  to  reach  the  desired  pass.  The 
only  remedy  in  such  a  case  is  by  a  resurvey  beginning  at  the  summit 
and  running  down  hill.  This  method  requires  a  reversal  of  that 
usually  adopted.  The  grade  line  is  first  staked  out  and  its  horizontal 
location  surveyed  afterwards.  The  most  appropriate  instrument  for 
this  work  is  a  transit  with  a  vertical  circle  on  which  the  telescope  may 
be  set  to  the  angle  of  the  maximum  grade. 

Loss  of  Height.  Loss  of  height 'is  to  be  carefully  avoided  in  a 
mountain  road.  By  loss  of  height  is  meant  an  intermediate  rise  in  a 
descending  grade.  If  a  descending  grade  is  interrupted  by  the  intro- 
duction of  an  unnecessary  ascent,  the  length  of  the  road  will  be  in- 
creased over  that  due  to  the  continuous  grade  by  the  length  of  the 
portion  of  the  road  intervening  between  the  summit  of  the  rise  and 
the  point  in  the  road  on  a  level  with  that  rise — a  length  which  is  double 
that  due  on  the  gradient  to  the  height  of  the  rise.  For  example, 
if  a  road  descending  a  mountain  rises  at  some  intermediate  point  to 
cross  over  a  ridge  or  spur,  and  the  height  ascended  amounts  to  110 
feet  before  the  descent  is  continued,  such  a  road  would  be  just  one 
mile  longer  than  if  the  descent  had  been  uninterrupted;  for  110  feet 
is  the  rise  due  to  a  half-mile  length  at  1 : 24. 

Water  on  Mountain  Roads.  Water  is  needed  by  the  work- 
men and  during  the  construction  of  the  road ;  it  is  also  very  necessary 
for  the  traffic,  especially  during  hot  weather;  and  if  the  road  exceeds 
5  miles  in  length,  provision  should  be  made  to  have  it  either  close 
to  or  within  easy  reach  of  the  road.  With  a  little  ingenuity  the 
water  from  springs  above  the  road,  if  such  exist,  can  be  led  down  to 
drinking  fountains  for  men,  and  to  troughs  for  animals. 

In  a  tropical  country  it  would  be  a  matter  for  serious  consider- 
ation if  the  best  line  for  a  mountain  road  10  miles  in  length  or  up- 
wards, but  without  water,  should  not  be  abandoned  in  favor  of  a 
worse  line  with  a  water  supply  available. 

Halting  Places.  On  long  lines  of  mountain  roads  halting 
places  should  be  provided  at  frequent  intervals. 


HIGHWAY  CONSTRUCTION  23 

Alignment.  No  rule  can  be  laid  down  for  the  alignment  of  a 
road;  it  will  depend  both  upon  the  character  of  the  traffic  on  it  and 
upon  the  "lay  of  the  land."  To  promote  economy  of  transportation 
it  should  be  straight;  but  if  s-traightness  is  obtained  at  the  expense 
of  easy  grades  that  might  have  been  obtained  by  deflections  and 
increase  in  length,  it  will  prove  very  expensive  to  the  community 
that  uses  it. 

Where  curves  are  necessary,  employ  the  greatest  radius  possible 
and  never  less  than  fifty  feet.  They  may  be  circular  or  parabolic. 
The  parabolic  will  be  found  exceedingly  useful  for  joining  tangents 
of  unequal  length,  and  for  following  contour  lines;  its  curvature 
being  least  at  its  beginning  and*  ending,  makes  the  deviations  from 
a  straight  line  less  strongly  marked  than  by  a  circular  arc. 

When  a  curve  occurs  on  an  ascent,  the  grade  at  that  place  must 
be  diminished  in  order  to  compensate  for  the  additional  resistance  of 
the  curve. 

The  width  of  the  wheel  way  on  curves  must  be  increased.  This 
increase  should  be  one-quarter  of  the  width  for  central  angles  between 
90  and  120  degrees,  and  one-half  for  angles  between  60  and  90  degrees. 
Excessive  crookedness  of  alignment  is  to  be  avoided,  for  any  unneces- 
sary length  causes  a  constant  threefold  wraste;  first,  of  the  interest 
of  the  capital  expended  in  making  that  unnecessary  portion;  secondly, 
of  the  ever  recurring  expense  of  repairing  it;  and  thirdly,  of  the  time 
and  labor  employed  on  travelling  over  it. 

.The  curving  road  around  a  hill  may  be  often  no  longer  than  the 
straight  one  over  it,  for  the  latter  is  straight  only  with  reference  to 
the  horizontal  plane,  while  it  is  curved  as  to  the  vertical  plane;  the 
former  is  curved  as  to  the  horizontal  plane,  but  straight  as  to  the 
vertical  plane.  Both  lines  curve,  and  we  call  the  one  passing  over 
the  hill  straight  only  because  its  vertical  curvature  is  less  apparent 
to  our  eyes. 

The  differen.ce  in  length  between  a  straight  road  and  one  which 
is  slightly  curved  is  very  small.  If  a  road  between  two  places  ten 
miles  apart  were  made  to  curve  so  that  the  eye  could  nowhere  see 
farther  than  one-quarter  of  a  mile  of  it  at  once,  its  length  would 
exceed  that  of  a  straight  road  between  the  same  points  by  only  about 
four  hundred  and  fifty  feet. 


24  HIGHWAY  CONSTRUCTION 

Zigzags.  The  method  of  surmounting  a  height  by  a  series  of 
zigzags  or  by  a  series  of  reaches  with  practicable  curves  at  the  turns, 
is  objectionable. 

(1)  An   acute-angled   zigzag  obliges   the   traffic   to   reverse  its 
direction  without  affording  it  convenient  room  for  the  purpose.     The 
consequence  is  that  with  slow  traffic  a  single  train  of  vehicles  is 
brought  to  a  stand,  while  if  two  trains  of  vehicles  travelling  in  opposite 
directions  meet  at  the  zigzag  a  block  ensues. 

(2)  With  zigzags  little  progress  is  made  towards  the  ultimate 
destination  of  the  road;  height  is  surmounted,  but  horizontal  distance 
is  increased  for  which  there  is  no  necessity  or  compensation. 

(3)  Zigzags  are  dangerous.     In  case  of  a  runaway  down  hill 
the  zigzag  must  prove  fatal. 

(4)  If  the  drainage  cannot  be  carried  clear  of  the  road  at  the 
end  of  each  reach,  it  must  be  carried  under  the  road  in  one  reach  only 
to  appear  again  at  the  next,  when  a  second  bridge,  culvert,  or  drain 
will  be  required,  and  so  on  at  the  other  reaches.     If  the  drainage  can 
be  carried  clear  at  the  termination  of  each  reach,  the  lengths  between 
the  curves  will  be  very  short,  entailing  numerous  zigzag  curves,  which 
are  expensive  to  construct  and  maintain. 

Final  Location.  The  route  being  finally  determined  upon,  it 
requires  to  be  located.  This  consists  in  tracing  the  line,  placing  a 
stake  at  every  100  feet  on  the  straight  portions  and  at  every  50  or 

25  feet  on  the  curves.     At  the  tangent  point  of  curves,  and  at  points 
of  compound  and  reverse  curves,  a  larger  and  more  permanent  stake 
should  be  placed.     Lest  those  stakes  should  be  disturbed  in  the 
process   of   construction,    their   exact   distance   from   several   points 
outside  of  the  ground  to  be  occupied  by  the  road  should  be  carefully 
measured  and  recorded  in  the  notebook,  so  that  they  may  be  replaced. 
The  stakes  above  referred  to  show  the  position  of  the  center  line  of 
the  road,  and  form  the  base  line  from  which  all  operations  of  con- 
struction are  carried  on.     Levels  are  taken  at  each  stake,"  and  cross 
levels  are  taken  at  every  change  of  longitudinal  slope. 

Construction  Profile.  The  construction  or  working  profile 
is  made  from  the  levels  obtained  on  location.  It  should  be  drawn  to  a 
horizontal  scale  of  400  feet  to  the  inch  and  a  vertical  scale  of  20  feet 
to  the  inch.  Fig.  7  represents  a  portion  of  such  a  profile.  The 


HIGHWAY  CONSTRUCTION 


figures  in  column  A  represent  the  elevation  of  the  ground  at  every 
100  feet,  or  where  a  stake  has  been  driven,  above  datum.  The 
figures  in  column  B  are  the  elevations  of  the  grade  above  datum. 
The  figures  in  column  C  indicate  the  depth  of  cutting  or  height  of 
fill;  they  are  obtained  by  taking  the  difference  between  the  level  of 
the  road  and  the  level  of  the  surface  of  the  ground.  The  straight  line 


STATION   NUMBERS 


at  the  top  represents  the  grade  of  the  road ;  the  upper  surface  of  the 
road  when  finished  would  be  somewhat  higher  than  this,  while  the 
given  line  represents  what  is  termed  the  sub-grade  or  formation  level. 
All  the  dimensions  refer  to  the  formation  level,  to  which  the  surface 
of  the  ground  is  to  be  formed  to  receive  the  road  covering. 

At  all  changes  in  the  rate  of  inclination  of  the  grade  line  a  heavier 
vertical  line  should  be  drawn. 

Gradient.  The  grade  of  a  line  is  its  longitudinal  slope,  and 
is  designated  by  the  proportion  between  its  length  and  the  difference 
of  height  of  its  two  extremes.  The  ratio  of  these  two  qualities  gives 
it  its  name;  if  the  road  ascends  or  falls  one  foot  in  every  twenty  feet 
of  its  length,  it  is  said  to  have  a  grade  of  1 :  20  or  a  5  per  cent  grade. 
Grades  are  of  two  kinds,  maximum  and  minimum.  The  maximum 
is  the  steepest  which  is  to  be  permitted  and  which  on  no  account  is  to  be 
exceeded.  The  minimum  is  the  least  allowable  for  good  drainage. 
(For  method  of  designating  grades  see  Table  9). 

Determination  of  Gradients.  The  maximum  grade  is  fixed 
by  two  considerations,  one  relating  to  the  power  expended  in  ascend- 
ing, the  other  to  the  acceleration  in  descending  the  incline. 

There  is  a  certain  inclination,  depending  upon  the  degree  of 
perfection  given  to  the  surface  of  the  road,  which  cannot  be  exceeded 


291 


26 


HIGHWAY  CONSTRUCTION 


without  a  direct  loss  of  tractive  power.  This  inclination  is  that  in 
descending  which,  at  a  uniform  speed,  the  traces  slacken,  or  which 
causes  the  vehicles  to  press  on  the  horses;  the  limiting  inclination 
within  which  this  effect  does  not  take  place  is  the  angle  of  repose. 


TABLE  9. 


American  method. 
Feet  per  100  feet. 

English  method. 

Feet  per  mile. 

Angle  with  the  horizon. 

l 

:400 

13.2 

0°     8'   36" 

| 

:200 

26.4 

0     17    11 

^ 

:150 

39.6 

0    22    55 

1 

100 

52.8 

0    34    23 

u 

80 

66 

0    42    58 

14 

66§ 

79.2 

0     51     28 

if 

57i 

92.4 

0    51 

2 

50 

105.6 

8      6 

2i 

44i 

118.8 

17    39 

2£ 

40 

132 

25    57 

2f 

36| 

145.2 

34    22 

3 

33| 

158.4 

43    08 

•H 

30f 

171.6 

51     42 

3i 

28^ 

184.8 

2       0    16 

3  f 

261 

198 

2       8    51 

4 

25 

211.2 

1     17    26 

4i 

234 

224.4 

2     26     1  0 

4i 

22i 

237.6 

2     34    36 

4f 

21 

250.8 

2    43    35 

5 

:    20 

264 

2     51     44 

6 

:    131 

316.8 

3     26    12 

7 

:    14l 

369  .  6 

4       0    15 

8 

1  :    m 

422.4 

4     34    26 

9 

1  :    Hi 

475.2 

5       8    31 

10 

1  :    10 

528 

5     42    37 

The  angle  of  repose  for  any  given  road  surface  can  be  easily 
ascertained  from  the  tractive  force  required  upon  a  level  with  the 
same  character  of  surface.  Thus  if  the  force  necessary  on  a  level 
to  overcome  the  resistance  of- the  load  is  TV  of  its  weight,  then  the 
same  fraction  expresses  the  angle  of  r-epose  for  that  surface. 

On  all  inclines  less  steep  than  the  angle  of  repose  a  certain 
amount  of  tractive  force  is  necessary  in  the  descent  as  well  as  in 
the  ascent,  and  the  mean  of  the  two  drawing  forces,  ascending  and 
descending,  is  equal  to  the  force  along  the  level  of  the  road.  Thus 
on  such  inclines,  as  much  mechanical  force  is  gained  in  the  descent 
as  is  lost  in  the  ascent.  From  this  it  might.be  inferred  that  when  a 
vehicle  passes  alternately  each  way  along  the  road,  no  real  loss  is 


HIGHWAY  CONSTRUCTION  27 

occasioned  by  the  inclination  of  the  road;  such  is  not,  however, 
practically  the  fact  with  animal  power,  for  while  it  is  necessary  in 
the  ascending  journey  to  have  either  a  less  or  a  greater  number  of 
horses  than  would  be  requisite  if  the  road  were  entirely  level,  no 
corresponding  reduction  can  be  made  in  the  descending  journey. 
On  inclines  which  are  more  steep  than  the  angle  of  repose,  the  load 
presses  on  the  horses  during  their  descent,  so  as  to  impede  their 
action,  and  their  power  is  expended  in  checking  the  descent  of  the 
load;  or  if  this  effect  be  prevented  by  the  use  of  any  form  of  drag  or 
brake,  then  the  power  expended  on  such  a  drag  or  brake  corresponds 
to  an  equal  quantity  of  mechanical  power  expended  in  the  ascent, 
for  which  no  equivalent  is  obtained  in  the  descent. 

The  maximum  grade  for  a  given  road  will  depend  (1)  upon  the 
class  of  traffic  that  will  use  it,  whether  fast  and  light,  slow  and  heavy, 
or  mixed,  consisting  of  both  light  and  heavy;  (2)  upon  the  character 
of  the  pavement  adopted;  and  (3)  upon  the  question  of  cost  of  con- 
struction. Economy  of  motive  power  and  low  cost  of  construction  are 
antagonistic  to  each  other,  and  the  engineer  will  have  to  weigh  the 
two  in  the  balance. 

For  fast  and  light  traffic  the  grades  should  not  exceed  2  per 
cent;  for  mixed  traffic  3  per  cent  may  be  adopted;  while  for  slow 
traffic  combined  with  economy  5  per  cent  should  not  be  exceeded. 
This  grade  is  practicable  but  not  convenient. 

Minimum  Grade.  From  the  previous  considerations  it  would 
appear  that  an  absolutely  level  road  wyas  the  one  to  be  sought  for,  but 
this  is  not  so;  there  is  a  minimum  or  least  allowable  grade  which  the 
road  must  not  fall  short  of,  as  well  as  a  maximum  one  which  it  must 
not  exceed.  If  the  road  was  perfectly  level  in  its  longitudinal  direc- 
tion, its  surface  could  not  be  kept  free  from  water  without  giving  it 
so  great  a  rise  in  its  middle  as  would  expose  vehicles  to  the  danger  of 
overturning.  The  minimum  grade  commonly  used  is  1  per  cent. 

Undulating  Grades.  From  the  fact  that  the  power  required 
to  move  a  load  at  a  given  velocity  on  a  level  road  is  decreased  on  a 
descending  grade  to  the  same  extent  it  is  increased  in  ascending  the 
same  grade,  it  must  not  be  inferred  that  the  animal  force  expended 
in  passing  alternately  each  way  over  a  rising  and  falling  road  will 
gain  as  much  in  descending  the  several  inclines  as  it  will  lose  in  ascend- 


28  HIGHWAY  CONSTRUCTION 

ing  them.  Such  is  not  the  case.  The»animal  force  must  be  sufficient, 
either  in  power  or  number,  to  draw  the  load  over  the  level  portions 
and  up  the  steepest  inclines  of  the  road,  and  in  practice  no  reduction 
in  the  number  of  horses  can  be  made  to  correspond  with  the  decreased 
power  required  in  descending  the  inclines. 

The  popular  theory  that  a  gentle  undulating  road  is  less  fatiguing 
to  horses  than  one  which  is  perfectly  level  is  erroneous.  The  asser- 
tion that  the  alternations  of  ascent,  descent,  and  levels  call  into  play 
different  muscles,  allowing  some  to  rest  while  others  are  exerted, 
and  thus  relieving  each  in  turn,  is  demonstrably  false,  and  con- 
tradicted by  the  anatomical  structure  of  the  horse.  Since  this  doc- 
trine is  a  mere  popular  error,  it  should  be  utterly  rejected,  not  only 
because  false  in  itself,  but  still  more  because  it  encourages  the  building 
of  undulating  roads,  and  this  increases  the  labor  and  cost  of  trans- 
portation upon  them. 

Level  Stretches.  On  long  ascents  it  is  generally  recom- 
mended to  introduce  level  or  nearly  level  stretches  at  frequent  inter- 
vals in  order  to  rest  the  animals.  These  are  objectionable  when 
they  cause  loss  of  height,  and  animals  will  be  more  rested  by  halting 
and  unharnessing  for  half  an  hour  than  by  travelling  over  a  level 
portion.  The  only  case  which  justifies  the  introduction  of  levels 
into  an  ascending  road  is  where  such  levels  will  advance  the  road 
towards  its  objective  point;  where  this  is  the  case  there  will  be  no 
loss  of  either  length  or  height,  and  it  will  simply  be  exchanging  a 
level  road  below  for  a  level  road  above. 

Establishing  the  Grade.  .  When  the  profile  of  a  proposed 
route  has  been  made,  a  grade  line  is  drawn  upon  it  (usually  in  red)  in 
such  a  manner  as  to  follow  its  general  slope,  but  to  average  its  irregular 
elevation  and  depressions. 

If  the  ratio  between  the  whole  distance  and  the  height  of  the  line 
is  less  than  the  maximum  grade  intended  to  be  used,  tins  line  will  be 
satisf acton*;  but  if  it  be  found  steeper,  the  cuttings  or  the  length 
of  the  line  will  have  to  be  increased ;  the  latter  is  generally  preferable. 

The  apex  or  meeting  point  of  all  curves  should  be  rounded  off 
by  a  vertical  curve,  as  showTi  in  Fig.  8,  thus  slightly  changing  the 
grade  at  and  near  the  point  of  intersection.  A  vertical  curve  rarely 
need  extend  more  than  200  feet  each  way  from  that  point. 


294 


HIGHWAY  CONSTRUCTION 


Let  A  B,  B  C,  be  two  grades  in  profile,  intersecting  at  station  B, 
and  let  A  and  C  be  the  adjacent  stations.     It  is  required  to  join  the 


Fig.  8. 

grades  by  a  vertical  curve  extending  from  A  to  C.  Imagine  a  chord 
drawn  from  A  to  C.  The  elevation  of  the  middle  point  of  the  chord 
will  be  a  mean  of  the  elevations  of  the  grade  at  A  and  C,  and  one- 
half  of  the  difference  between  this  and  the  elevation  of  the  grade  at 
B  will  be  the  middle  ordinate  of  the  curve.  Hence  we  have 


in  which  M  equals  the  correction  in  grade  for  the  point  B.  The 
correction  for  any  other  point  is  proportional  to  the  square  of  its 
distance  from  A  or  C.  Thus  the  correction  A+  25.  isTVM;  at 
A  -H  50  it  is  i  M;  at  A  +  75  it  is  T9^  M;  and  the  same  for  corre- 
sponding points  on  the  other  side  of  B.  The  corrections  in  this  case 
shown  are  subtractive,  since  M  is  negative.  They  are  additive 
when  M  is  positive,  and  the  curve  concave  upward. 

WIDTH  AND  TRANSVERSE  CONTOUR. 

A  road  should  be  wide  enough  to  accommodate  the  traffic  for 
which  it  is  intended,  and  should  comprise  a  wheelway  for  vehicles 
and  a  space  on  each  side  for  pedestrians. 

The  wheelway  of  country  highways  need  be  no  wider  than  is 
absolutely  necessary  to  accommodate  the  traffic  using  it;  in  many 
places  a  track  wide  enough  for  a  single  team  is  all  that  is  necessary. 
But  the  breadth  of  the  land  appropriated  for  highway  purposes 
should  be  sufficient  to  provide  for  all  future  increase  of  traffic.  The 
wheel  ways  of  roads  in  rural  sections  should  be  double;  that  is,  one 
portion  paved  (preferably  the  center),  and  the  other  left  with  the 


30  HIGHWAY  CONSTRUCTION 

natural  soil.  The  latter  if  kept  in  repair  will  for  at  least  one-half 
the  year  be  preferred  by  teamsters. 

The  minimum  width  of  the  paved  portion,  if  intended  to  carry 
two  lines  of  travel,  is  fixed  by  the  width  required  to  allow  two  vehicles 
to  pass  each  other  safely.  This  width  is  16  feet.  If  intended  for 
a  single  line  of  travel,  8  feet  is  sufficient,  but  suitable  turnouts  must  be 
provided  at  frequent  intervals.  The  most  economical  width  for  any 
roadway  is  some  multiple  of  eight. 

Wide  roads  are  the  best;  they  expose  a  larger  surface  to  the 
drying  action  of  the  sun  and  wind,  and  require  less  supervision  than 
narrow  ones.  Their  first  cost  is  greater  than  narrow  ones,  and  that 
nearly  in  the  ratio  of  the  increased  width. 

The  cost  of  maintaining  a  mile  of  road  depends  more  upon  the 
extent  of  the  traffic. than  upon  the  extent  of  its  surface,  and  unless 
extremes  be  taken,  the  same  quantity  of  material  will  be  necessary 
for  the  repair  of  the  road  whether  wide  or  narrow,  which  is  subjected 
to  the  same  amount  of  traffic.  The  cost  of  spreading  the  materials 
over  the  wide  road  will  be  somewhat  greater,  but  the  cost  of  the 
materials  will  be  the  same.  On  narrow  roads  the  traffic,  being 
confined  to  one  track,  will  wear  more  severely  than  if  spread  over  a 
wider  surface. 

The  width  of  land  appropriated  for  road  purposes  varies  in  the 
United  States  from  49^  feet  to  66  feet;  in  England  and  France  from 
26  to  66  feet.  And  the  width  or  space  macadamized  is  also  subject 
to  variation;  in  the  United  States  the  average  width  is  16  feet;  in 
France  it  varies  between  16  and  22  feet;  in  Belgium  8J  feet  seems 
to  be  the  regular  width,  while  in  Austria  from  14^  to  26|  feet. 

Transverse  Contour.  The  center  of  all  roadways  should 
be  higher  than  the  sides.  The  object  of  this  is  to  facilitate  the  flow 
of  the  rain  water  to  the  gutters.  Where  a  good  surface  is. maintained 
a  very  moderate  amount  of  rise  is  sufficient  for  this  purpose.  Earth 
roads  require  the  most  and  asphalt  the  least.  The  rise  should  bear 
a  certain  proportion  to  the  width  of  the  carriageway.  The  most 
suitable  proportions  for  the  different  paving  materials  is  shown  in 
table  10. 

Form  of  Transverse  Contour.  All  authorities  agree  that 
the  form  should  be  convex,  but  they  differ  in  the  amount  and  form 


806 


HIGHWAY  CONSTRUCTION  31 

of  the  convexity.     Circular  arcs,  two  straight  lines  joined  by  a  circular 
arc,  and  ellipses,  all  have  their  advocates. 

TABLE  10. 

Kind  of  Surface.  Proportions  of  the 

Carriageway.  Width. 

Earth  Rise  at  center  ¥V 

Gravel  ^ 

Broken  Stone  ^ 

For  country  roads  a  curve  of  suitable  convexity  may  be  obtained 
as  follows:  Give  |  of  the  total  rise  at  \  the  width  from  the  center 
to  the  side,  and  f  of  the  total  rise  at  ^  the  width  (Fig.  9). 

Excessive  height  and  convexity  of  cross-section  contract  the 
width  of  the  wheelway,  by  concentrating  the  traffic  at  the  center, 
that  being  the  only  part  where  a  vehicle  can  run  upright.  The  force' 
required  to  haul  vehicles  over  such  cross-sections  is  increased,  be- 


Fig.   9. 

cause  an  undue  proportion  of  the  load  is  thrown  upon  two  wheels 
instead  of  being  distributed  equally  over  the  four.  The  continual 
tread  of  horses'  feet  in  one  track  soon  forms  a  depression  which  holds 
water,  and  the  surface  is  not  so  dry  as  with  a  flat  section,  which  allows 
the  traffic  to  distribute  itself  over  the  whole  width. 

Sides  formed  of  straight  lines  are  also  objectionable.  They 
wear  hollow,  retain  water,  and  defeat  the  object  sought  by  raising 
the  center. 

The  required  convexity  should  be  obtained  by  rounding  the 
formation  surface,  and  not  by  diminishing  the  thickness  of  the 
covering  at  the  sides. 

Although  on  hillside  and  mountain  roads  it  is  generally  recom- 
mended that  the  surface  should  consist  of  a  single  slope  inclining 
inwards,  there  is  no  reason  for  "or  advantage  gained  by  this  method. 
The  form  best  adapted  to  these  roads  is  the  same  as  for  a  road  under 
ordinary  conditions. 

With  a  roadway  raised  in  the  center  and  the  rain  water  draining 
off  to  gutters  on  each  side,  the  drainage  will  be  more  effectual  and 


32  HIGHWAY  CONSTRUCTION 

speedy  than  if  the  drainage  of  the  outer  half  of  the  road  has  to  pass 
over  the  inner  half.  The  inner  half  of  such  a  road  is  usually  sub- 
jected to  more  traffic  than  the  outer  half.  If  formed  of  a  straight 
incline,  this  side  will  be  worn  hollow  and  retain  water.  The  inclined 
flat  section  never  can  be  properly  repaired  to  withstand  the  traffic. 
Consequently  it  never  can  be  kept  in  good  order,  no  matter  how 
constantly  it  may  be  mended.  It  is  always  below  par  and  when 
heavy  rain  falls  it  is  seriously  damaged. 
DRAINAGE. 

In  the  construction  of  roads,  drainage  is  of  the  first  importance. 
The  ability  of  earth  to  sustain  a  load  depends  in  a  large  measure  upon 
the  amount  of  moisture  retained  by  it.  Most  earths  form  a  good 
firm  foundation  so  long  as  they  are  kept  dry,  but  when  wet  they  lose 
their  sustaining  power,  becoming  soft  and  incoherent. 

The  drainage  of  roadways  is  of  two  kinds,  viz.,  surface  and  sub- 
surface. The  first  provides  for  the  speedy  removal  of  all  water 
falling  on  the  surface  of  the  road;  the  second  provides  for  the  removal 
of  the  underground  water  found  in  the  body  of  the  road,  a  thorough 
removal  of  which  is  of  the  utmost  importance  and  essential  to  the 
life  of  the  road.  A  road  covering  placed  on  a  wet  undrained  bottom 
will  be  destroyed  by  both  water  and  frost,  and  will  always  be  trouble- 
some and  expensive  to  maintain;  perfect  subsoil  drainage  is  a  neces- 
sity and  will  be  found  economical  in  the  end  even  if  in  securing  it 
considerable  expense  is  required. 

The  methods  employed  for  securing  the  subsoil  drainage  must 
be  varied  according  to  the  character  of  the  natural  soil,  each  kind  of 
soil  requiring  different  treatment. 

The  natural  soil  may  be  divided  into  the  following  classes: 
silicious,  argillaceous,  and  calcareous;  rock,  swamps,  and  morasses. 

The  silicious  and  calcareous  soils,  the  sandy  loams  and  rock, 
present  no  great  difficulty  in  securing  a  dry  and  solid  foundation. 
Ordinarily  they  are  not  retentive  of  water  and  therefore  require  no 
underdrains;  ditches  on  each  side  of  the  road  will  generally  be  found 
sufficient. 

The  argillaceous  soils  and  softer  marls  require  more  care;  they 
retain  water  and  are  difficult  to  compact,  except  at  the  surface; 
and  they  are  very  unstable  under  the  action  of  water  and  frost. 


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HIGHWAY  CONSTRUCTION 


The  drainage  of  these  soils  may  be  effected  by  transverse  drains 
and  deep  side  ditches  of  ample  width.  The  transverse  drains  are 
placed  across  the  road,  not  at  right  angles  but  in  the  form  of  an 
inverted  V  with  the  point  directed  up  hill;  the  depth  at  the  angle 
point  should  not  be  less  than  18  inches  below  the  subgrade  surface, 
and  each  branch  should  descend  from  the  apex  to  the  side  ditches 
with  a  fall  of  not  less  than  1  inch  in  5  feet.  The  distance  apart  of 
these  drains  will  depend  upon  the  wetness  of  the  soil;  in  the  case  of 
very  wet  soil  they  should  be  at  intervals  of  15  feet,  which  may  be 
increased  to  25  feet  as  the  ground  becomes  drier  and  firmer. 

The  transverse  drains  are  best  formed  of  unglazed  circular  tile 
of  a  diameter  not  less  than  3  inches,  jointed  with  loose  collars.  The 
tiles  are  made  from  terra  cotta  or  burnt  clay,  are  porous,  and  are 
superior  to  all  other  kinds  of  drains.  They  carry  off  the  water  with 
greater  ease,  rarely  if  ever  get  choked  up,  and  only  require  a  slight 
inclination  to  keep  the  water  moving  through  them. 


Fig.  10.    Tile  Drain. 


Fig.  11.    Silt  Basin. 

The  tiles  are  made  in  a  variety  of  forms,  as  horseshoe,  sole, 
double  sole,  and  round,  the  name  being  derived  from  the  shape  of 
the  cross-sections.  Round  tile  is  superior  to  all  other  forms.  The 
inside  diameter  of  these  tiles  varies  from  1£  to  6  inches,  but  they  are 
manufactured  as  large  as  24  inches.  Pieces  of  the  larger  pipe  serve 
as  collars  for  the  smaller  ones.  They  are  made  in  lengths  of  12, 
14  and  24  inches,  and  in  thickness  of  shell  from  ^"of  an  inch  to  1  inch. 

The  collar  which  encircles  the  joint  of  the  small  tile  allows  a 
large  opening,  and  at  the  same  time  prevents  sand  and  silt  from 


290 


HIGHWAY  CONSTRUCTION 


entering  the  drain.  Perishable  material  should  not  be  used  for 
jointing.  When  laid  in  the  ditch  they  should  be  held  in  place  by 
small  stones.  Connections  should  be  made  by  proper  Y-branches. 
The  outlets  may  be  formed  by  building  a  dwarf  wall  of  brick  or 
stone,  whichever  is  the  cheapest  or  most  convenient  in  the  locality. 
The  outlet  should  be  covered  with  an  iron  grating  to  prevent  vermin 
entering  the  drain  pipes,  building  nests  and  thus  choking  up  the 
waterway.  (See  Fig.  12.) 


Fig.  12.     Outlet. 

Silt-basins  should  be  constructed  at  all  junctions  and  wherever 
else  they  may  be  considered  necessary;  they  may  be  made  from  a 
single  6-inch  pipe  (Fig.  11)  or  constructed  of  brick  masonry. 

The  trenches  for  the  tile  should  be  excavated  at  least  3  feet 
wide  on  top  and  12  inches  on  the  bottom.  After  the  tiles  are  laid 
the  trenches  must  be  filled  to  subgrade  level  with  round  field  or 
cobble  stones;  stones  with  angular  edges  are  unsuitable  for  this 
purpose.  Fine  gravel,  sand,  or  soil  should  not  be  placed  over  the 
drains.  Bricks  and  flat  stones  may  be  substituted  for  the  tiles, 
and  the  trenches  filled  as  above  stated. 

As  tile  drains  are  more  liable  to  injury  from  frost  than  those 
of  either  brick  or  stone,  their  ends  at  the  side  ditches  should  not 
in  very  cold  climates  be  exposed  directly  to  the  weather,  but  may 
terminate  in  blind  drains,  or  a  few  lengths  of  vitrified  clay  pipe 
reaching  under  the  road  a  distance  of  about  3  to  4  feet  from  the 
inner  slope  of  the  ditch. 

Another  method  of  draining  the  roadbed  offering  security  from 
frost  is  by  one  or  more  rows  of  longitudinal  drains.  These  drains 
are  placed  at  equal  distances  from  the  side  ditches  and  from  each 
other,  and  discharge  into  cross  drains  placed  from  250  to  300  feet 


800 


HIGHWAY  CONSTRUCTION 


apart,  more  or  less,  depending  on  the  contour  of  the  ground.  The 
cross  drains  into  which  they  discharge  should  be  of  ample  dimensions. 
On  these  longitudinal  lines  of  tiles  the  introduction  of  catch  basins 
at  intervals  of  50  feet  will  facilitate  the  removal  of  the  water.  These 
catch  basins  may  be  excavated  three  or  more  feet  square  and  as  deep 
as  the  tiles  are  laid.  After  the  tiles  are  laid  the 'pit  is  filled  with  gravel 
and  small  stones. 


Fig.  13. 

Fall  of  Drains.  It  is  a  mistake  to  give  too  much  fall  to  small 
drains,  the  only  effect  of  which  is  to  produce  such  a  current  through 
them  as  will  wash  away  or  undermine  the  ground  around  them,  and 
ultimately  cause  their  own  destruction.  When  a  drain  is  once  closed 
by  any  obstruction  no  amount  of  fall  which  could  be  given  it  will 


Fig.  14. 

again  clear  the  passage.  A  drain  with  a  considerable  current  through 
it  is  much  more  likely  to  be  stopped  from  foreign  matter  carried  into 
it,  which  a  less  rapid  stream  could  not  have  transported. 

A  fall  of  1  inch  in  5  feet  wrill  generally  be  sufficient,  and  1  inch 
in  30  inches  should  never  be  exceeded. 


Fig.  15. 

Side  Ditches  are  provided  to  carry  away  the  subsoil  water 
from  the  base  of  the  road,  and  the  rain  water  which  falls  upon  its 
surface;  to  do  this  speedily  they  must  have  capacity  and  inclination 


301 


36 


HIGHWAY  CONSTRUCTION 


proportionate  to  the  amount  of  water  reaching  them.  The  width 
of  the  bed  should  not  be  less  than  18  inches;  the  depth  will  vary  with 
circumstances,  but  should  be  such  that  the  water  surface  shall  not 
reach  the  subgrade,  but  remain  at  least  12  inches  below  the  crown 
of  the  road.  The  sides  should  slope  at  least  1£  to  1. 

The  longitudinal  inclination  of  the  ditch  follows  the  configura- 
tion of  the  general  topography,  that  is,  the  lines  of  natural  drainage. 
When  the  latter  has  to  be  aided  artificially,  grades  from  1  in  500  to 
1  in  800  will  usually  answer. 


Fig.  16. 

In  absorbent  soil  less  fall  is  sufficient,  and  in  certain  cases  level 
ditches  are  permissible.  The  slopes  of  the  ditches  must  be  protected 
where  the  grade  is  considerable.  This  can  be  accomplished  by  sod 
revetments,  riprapping,  or  paving. 

These  ditches  may  be  placed  either  on  the  road  or  land  side  of  the 
fence.  In  localities  where  open  ditches  are  undesirable  they  may  be 
constructed  as  shown  in  Figs.  13  to  17,  and  may  be  formed  of  stone 


Fig.  17. 

or  tile  pipe,  according  to  the  availability  of  either  material.  If  for 
any  reason  two  can  not  be  built,  build  one. 

Springs  found  in  the  roadbed  should  be  tapped  and  led  into  the 
side  ditches. 

Drainage  of  the  Surface.  The  drainage  of  the  roadway 
surface  depends  upon  the  preservation  of  the  cross-section,  with 
regular  and  uninterrupted  fall  to  the  sides,  without  hollows  or  ruts 
in  which  the  water  can  lie,  and  also  upon  the  longitudinal  fall  of  the 


302 


HIGHWAY  CONSTRUCTION  37 

road.  If  this  is  not  sufficient  the  road  becomes  flooded  during  heavy 
rainstorms  and  melting  snow,  and  is  considerably  damaged. 

The  removal  of  surface  water  from  country  roads  may  be  effected 
by  the  side  ditches,  into  which,  when  there  are  no  sidewalks,  the 
water  flows  directly.  When  there  are  sidewalks,  gutters  are  formed 
between  the  roadway  and  footpath,  as  shown  in  Figs.  13  to  17,  and 
the  water  is  conducted  from  these  gutters  into  the  side  ditches  by 
tile  pipes  laid  under  the  walks  at  intervals  of  about  50  feet.  The 
entrance  to  these  pipes  should  be  protected  against  washing  by  a 
rough  stone  paving.  In  the  case  of 'covered  ditches  under  the  footpath 
the  water  must  be  led  into  them  by  first  passing  through  a  catch 
basin.  These  are  small  masonry  vaults  covered  with  iron  gratings  to 
prevent  the  ingress  of  stones,  leaves,  etc.  Connection  from  the 
catch  basin  is  made  by  a  tile  pipe  about  6  inches  in  diameter.  The 
mouth  of  this  pipe  is  placed  a  few  feet  above  the  bottom  of  the  catch 
basin,  and  the  space  below  it  acts  as  a  depository  for  the  silt  carried 
by  the  water,  and  is  cleaned  out  periodically.  The  catch  basins  may 
be  placed  from  200  to  300  feet  apart.  They  should  be  made  of 
dimensions  sufficient  to  convey  the  amount  of  water  which  is  liable 
to  flow  into  them  during  heavy  and  continuous  rains. 

If  on  inclines  the  velocity  of  the  water  is  greater  than  the  nature 
of  the  soil  will  withstand,  the  gutters  will  be  roughly  paved.  In  all 
cases,  the  slope  adjoining  the  footpath  should  be  covered  with  sod. 

A  velocity  of  30  feet  a  minute  will  not  disturb  clay  with  sand  and 
stone.  40  feet  per  minute  will  move  coarse  sand.  60  feet  a  minute 
will  move  gravel.  120  feet  a  minute  should  move  round  pebbles  1  inch 
in  diameter,  and  180  feet  a  minute  will  move  angular  stones  If  inches 
in  diameter. 

The  scour  in  the  gutters  on  inclines  may  be  prevented  by  small 
weirs  of  stones  or  fascines  constructed  by  the  roadmen  at  a  nominal 
cost.  At  junctions  and  crossroads  the  gutters  and  side  ditches  re- 
quire careful  arrangement  so  that  the  water  from  one  road  may  not 
be  thrown  upon  another;  cross  drains  and  culverts  will  be  required 
at  such  places. 

Water  Breaks  to  turn  the  surface  drainage  into  the  side  ditches 
should  not  be  constructed  on  improved  roads.  They  increase  the 
grade  and  are  an  impediment  to  convenient  and  easy  travel.  Where 


303 


38  HIGHWAY  CONSTRUCTION 

it  is  necessary  that  water  should  cross  the  road  a  culvert  should  be 
built. 

On  the  side  hill  or  mountain  roads  catch-water  ditches  should 
be  cut  on  the  mountain  side  above  the  road,  to  cut  off  and  convey  the 
drainage  of  the  ground  above  them  to  the  neighboring  ravines.  The 
size  of  these  ditches  will  be  determined  by  the  amount  of  rainfall, 
extent  of  drainage  from  the  mountain  which  they  intercept,  and  by  the 
distances  of  the  ravine  water  courses  on  each  side. 

The  inner  road  gutter  should  be  of  ample  dimensions  to  carry 
off  the  water  reaching  it;  when  in  soil,  it  should  be  roughly  paved  with 
stone.  When  paving  is  not  absolutely  necessary,  but  it  is  desirable 
to  arrest  the  scouring  action  of  running  water  during  heavy  rains, 
stone  weirs  may  be  erected  across  the  gutter  at  convenient  intervals. 
The  outer  gutter  need  not  be  more  than  12  inches  wide  and  9  inches 
deep.  The  gutter  is  formed  by  a  depression  in  the  surface  of  the 
road  close  to  the  parapet  or  revetted  earthen  protection  mound.  The 
drainage  which  falls  into  this  gutter  is  led  off  through  the  parapet, 
or  other  roadside  protection  at  frequent  intervals.  The  guard  stones 
on  the  outside  of  the  road  are  placed  in  and  across  this  gutter,  just 
below  the  drainage  holes,  so  as  to  turn  the  current  of  the  drainage 
into  these  holes  or  channels.  On  straight  reaches,  with  parapet 
protection,  drainage  holes  with  guard  stones  should  be  placed  every 
20  feet  apart.  Where  earthen  mounds  are  used  and  it  may  not  be 
convenient  to  have  the  drainage  holes  or  channels  every  20  feet,  the 
guardstones  are  to  be  placed  in  advance  of  the  gutter  to  allow  the 
drainage  to  pass  behind  them,  This  drainage  is  either  to  be  run  off 
at  the  cross  drainage  of  the  road,  or  to  be  turned  off  as  before  by  a 
guard  stone  set  across  the  gutter. 

At  re-entering  turns,  where  the  outer  side  of  the  road  requires 
particular  protection,  guard  stones  should  be  placed  every  4  feet. 
As  all  re-entering  turns  should  be  protected  by  parapets,  the  drainage 
holes  through  them  may  be  placed  as  close  together  as  desired. 

Culverts  are  necessary  for  carrying  under  a  road  the  streams 
it  crosses,  and  also  for  conveying  the  surface  water  collected  in  the 
side  ditches  from  the  upper  side  to  that  side  on  which  the  natural 
water  courses  lie. 

Especial  care  is  required  to  provide  an  ample  way  for  the  water 


304 


HIGHWAY  CONSTRUCTION 


to  be  passed.  If  the  culvert  is  too  small,  it  is  liable  to  cause  a  washout, 
entailing  interruption  of  traffic  and  cost  of  repairs,  and  possibly  may 
cause  accidents  that  will  require  payment  of  large  sums  for  damages. 
On  the  other  hand,  if  the  culvert  is  made  unnecessarily  large,  the 
cost  of  construction  is  needlessly  increased. 

The  area  of  waterway  required  depends  (1)  upon  the  rate  of 
rainfall;  (2)  the  kind  and  condition  of  the  soil;  (3)  the  character 
and  inclination  of  the  surface;  (4)  the  condition  and  inclination  of 
the  bed  of  the  stream;  (5)  the  shape  of  the  area  to  be  drained,  and 
the  position  of  the  branches  of  the  stream;  (6)  the  form  of  the  mouth 
and  the  inclination  of  the  bed  of  the  culvert;  and  (7)  whether  it  is 
permissible  to  back  the  water  up  above  the  culvert,  thereby  causing 
it  to  discharge  under  a  head. 

(1)  It  is  the  maximum  rate  of  rainfall  during  the  severest  storms 
which  is  required  in  this  connection.     This  varies  greatly  in  different 
sections  of  the  country. 

The  maximum  rainfall  as  shown  by  statistics  is  about  one  inch 
per  hour  (except  during  heavy  storms),  equal  to  3,630  cubic  feet  per 
acre.  Owing  to  various  causes,  not  more  than  50  to  75  per  cent  of 
this  amount  will  reach  the  culvert  within  the  same  hour. 

Inches  of  rainfall  X  3,630  =  cubic  feet  per  acre. 

Inches  of  rainfall  X  2,323,200  =  cubic  feet  per  square  mile. 

(2)  The  amount  of  water  to  be  drained  off  will  depend  upon  the 
permeability  of  the  surface  of  the  ground,  which  will  vary  greatly 
with  the  kind  of  soil,  the  degree  of  saturation,  the  condition  of  the 
cultivation,  the  amount  of  vegetation,  etc. 

(3)  The  rapidity  with  which  the  water  will  reach  the  water 
course  depends  upon  whether  the  surface  is  rough  or  smooth,  steep 
or  flat,  barren  or  covered  with  vegetation,  etc. 

(4)  The  rapidity  with  which  the  water  will  reach  the  culvert 
depends  upon   whether  there   is   a  well-defined   and   unobstructed 
channel,  or  whether  the  water  finds  its  way  in  a  broad  thin  sheet. 
It  the  water  course  is  unobstructed  and  has  a  considerable  inclination, 
the  water  may  arrive  at  the  culvert  nearly  as  rapidly  as  it  falls;  but 
if  the  channel  is  obstructed,  the  water  may  be  much  longer  in  passing 
the  culvert  than  in  falling. 

(5)  The  area  of  waterway  depends  upon  the  amount  of  the  area 


305 


40  HIGHWAY  CONSTRUCTION 

to  be  drained ;  but  in  many  cases  the  shape  of  this  area  and  the  posi- 
tion of  the  branches  of  the  stream  are  of  more  importance  than  the 
amount  of  the  territory.  For  example,  if  the  area  is  long  and  narrow, 
the  water  from  the  lower  portion  may  pass  through  the  culvert  before 
that  from  the  upper  end  arrives;  or,  on  the  other  hand,  if  the  upper 
end  of  the  area  is  steeper  than  the  lower,  the  water  from  the  former 
may  arrive  simultaneously  with  that  from  the  latter.  Again,  if  the 
lower  part  of  the  area  is  better  supplied  with  branches  than  the  upper 
portion,  the  water  from  the  former  will  be  carried  past  the  culvert 
before  the  arrival  of  that  from  the  latter;  or,  on  the  other  hand,  if 
the  upper  part  is  better  supplied  with  branch  water  courses  than 
the  lower,  the  water  from  the  whole  area  may  arrive  at  the  culvert 
at  nearly  the  same  time.  In  large  areas  the  shape  of  the  area  and 
the  position  of  the  water  courses  are  very  important  considerations. 

(6)  The  efficiency  of  a  culvert  may  be  very  materially  increased 
by  so  arranging  the  upper  end  that  the  water  may  enter  into  it  without 
being  retarded.     The  discharging  capacity  of  a  culvert  can  be  greatly 
increased  by  increasing  the  inclination  of  its  bed,  provided  the  channel 
below  will  allow  the  water  to  flow  away  freely  after  having  passed 
the  culvert. 

(7)  The  discharging  capacity  of  a  culvert  can  be  greatly  increased 
by  allowing  the  water  to  dam  up  above  it.     A  culvert  will  discharge 
twice  as  much  under  a  head  of  four  feet  as  under  a  head  of  one  foot. 
This  can  be  done  safely  only  with  a  well  constructed  culvert. 

The  determination  of  the  values  of  the  different  factors  entering 
into  the  problem  is  almost  wholly  a  matter  of  judgment.  An  estimate 
for  any  one  of  the  above  factors  is  liable  to  be  in  error  from  100  to 
200  per  cent,  or  even  more,  and  of  course  any  result  deduced  from 
such  data  must  be  very  uncertain.  Fortunately,  mathematical  exact- 
ness is  not  required  by  the  problem  nor  warranted  by  the  data.  The 
question  is  not  one  of  10  or  20  per  cent  of  increase;  for  if  a  2-foot  pipe 
is  sufficient,  a  3-foot  pipe  will  probably  be  the  next  size,  an  increase 
of  225  per  cent;  and  if  a  6-foot  arch  culvert  is  too  small,  an  8-foot  will 
be  used,  an  increase  of  180  per  cent.  The  real  question  is  whether 
a  2-foot  pipe  or  an  8-foot  arch  culvert  is  needed. 

Valuable  data  on  the  proper  size  of  any  particular  culvert  may 
be  obtained  (1)  by  observing  the  existing  openings  on  the  same 


306 


HIGHWAY  CONSTRUCTION  41 

stream ;  (2)  by  measuring,  preferably  at  time  of  high  water,  a  cross- 
section  of  the  stream  at  some  narrow  place;  and  (3)  determining  the 
height  of  high  water  as  indicated  by  drift  and  the  evidence  of  the 
inhabitants  of  the  neighborhood. 

On  mountain  roads  or  roads  subjected  to  heavy  rainfall  culverts 
of  ample  dimensions  should  be  provided  wherever  required,  and  it 
will  be  more  economical  to  construct  them  of  masonry.  In  localities 
where  boulders  and  other  debris  are  likely  to  be  washed  down  during 
wet  weather,  it  will  be  a  good  precaution  to  construct  catch  pools  at 
the  entrance  of  all  culverts  and  cross  drains  for  the  reception  of 
such  matter.  In  hard  soil  or  rock  these  catch  pools  will  be  simple 
\vell-like  excavations,  with  their  bottom  two  or  three  feet  below  the 
entrance  sill  or  floor  of  the  culvert  or  drain.  Where  the  soil  is  soft 
they  should  be  lined  with  stone  laid  dry;  if  very  soft,  with  masonry. 
The  size  of  the  catch  pools  will  depend  upon  the  width  of  the  drainage 
works.  They  should  be  wide  enough  to  prevent  the  drains  from 
being  injured  by  falling  rocks  and  stones  of  a  not  inordinate  size. 

The  use  of  catch  pools  obviates  the  necessity  of  building  culverts 
and  drains  at  an  angle  to  the  axis  of  the  road.  Oblique  structures 
are  objectionable,  as  being  longer  than  if  set  at  right  angles  and  by 
reason  of  the  acute-  and  obtuse-angled  terminations  to  their  piers, 
abutments,  and  coverings. 

Materials  for  Culverts.  Culverts  may  be  of  stone,  brick,  vitri- 
fied earthenware,  or  iron  pipe.  Wood  should  be  absolutely  avoided. 

For  small  streams  and  a  limited  surface  of  rainfall  either  class 
of  pipes,  in  sizes  varying  from  12  to  24  inches  in  diameter,  will  serve 
excellently.  They  are  easily  laid,  and  if  properly  bedded,  with  the 
earth  tamped  about  them,  are  very  permanent.  Their  upper  surface 
should  be  at  least  18  inches  below  the  road  surface,  and  the  upper 
end  should  be  protected  with  stone  paving  so  arranged  that  the  water 
can  in  no  case  work  in  around  the  pipe. 

When  the  flow  of  water  is  estimated  to  be  too  great  for  two  lines 
of  24-inch  pipes,  a  culvert  is  required.  If  stone  abounds,  it  may  be 
built  of  large  roughly  squared  stones  laid  either  dry  or  in  mortar. 
When  the  span  required  is  more  than  5  feet,  arch  culverts  either  of 
stone  or  brick  masonry  may  be  employed.  For  spans  above  15  feet 
the  structure  required  becomes  a  bridge 


307 


42 


HIGHWAY  CONSTRUCTION 


Earthenware  Pipe  Culverts.  Construction.  In  laying  the 
pipe  the  bottom  of  the  trench  should  be  rounded  out  to  fit  the  lower 
half  of  the  body  of  the  pipe  with  proper  depressions  for  the  sockets. 
If  the  ground  is  soft  or  sandy,  the  earth  should  be  rammed  carefully, 
but  solidly  in  and  around  the  lower  part  of  the  pipe.  The  top  surface 
of  the  pipe  should,  as  a  rule,  never  be  less  than  18  inches  below  the 
surface  of  the  roadway,  but  there  are  many  cases  where  pipes  have 
stood  for  several  years  under  heavy  loads  with  only  8  to  12  inches  of 
earth  over  them.  No  danger  from  frost  need  be  apprehended,  pro- 
vided the  culverts  are  so  constructed  that  the  water  is  carried  away 
from  the  level  end.  Ordinary  soft  drain  tiles  are  not  in  the  least 
affected  by  the  expansion  of  frost  in  the  earth  around  them. 

The  freezing  of  water  in  the  pipe,  particularly  if  more  than  half 
full,  is  liable  to  burst  it;  consequently  the  pipe  should  have  a  suffi- 
cient fall  to  drain  itself,  and  the  outside  should  be  so  low  that  there 
is  no  danger  of  back  waters  reaching  the  pipe.  If  properly  drained, 
there  is  no  danger  from  frost. 

Jointing.  In  many  cases,  perhaps  in  most,  the  joints  are 
not  calked.  If  this  is  not  done,  there  is  liability  of  the  water  being 
forced  out  of  the  joints  and  washing  away  the  soil  from  around  the 
pipe.  Even  if  the  danger  is  not  very  imminent,  the  joints  of  the 
larger  pipes,  at  least,  should  be  calked  with  hydraulic  cement,  since 
the  cost  is  very  small  compared  with  the  insurance  against  damage 


Fig.  18. 

thereby  secured.  Sometimes  the  joints  are  calked  with  clay.  Every 
culvert  should  be  built  so  that  it  can  discharge  water  under  a  head 
without  damage  to  itself. 


308 


HIGHWAY  CONSTRUCTIOX 


Although  often  omitted,  the  end  sections  should  be  protected 
with  a  masonry  or  timber  bulkhead.  The  foundation  of  the  bulk- 
head should  be  deep  enough  not  to  be  disturbed  by  frost.  In  con- 
structing the  end  wall,  iJ;  is  well  to  increase  the  fall  near  the  outlet 
to  allow  for  a  possible  settlement  of  the  interior  sections.  When 
stone  and  brick  abutments  are  too  expensive,  a  fair  substitute  can 
be  made  by  setting  posts  in  the  ground  and  spiking  plank  to  them. 
When  planks  are  used,  it  is  best  to  set  them  with  considerable  inclina- 
tion towards  the  roadbed  to  prevent  their  being  crowded  outward 
by  the  pressure  of  the  embankment.  The  upper  end  of  the  culvert 
should  be  so  protected  that  the  water  will  not  readily  find  its  way 


Fig.  19. 

along  the  outside  of  the  pipes,  in  case  the  mouth  of  the  culvert  should 
become  submerged. 

When  the  capacity  of  one  pipe  is  not  sufficient,  two  or  more 
may  be  laid  side  by  side  as  shown  in  Fig.  19.  Although  the  two 
small  pipes  do  not  have  as  much  discharging  capacity  as  a  single 
large  one  of  equal  cross-section,  yet  there  is  an  advantage  in  laying 
two  small  ones  side  by  side,  since  the  water  need  not  rise  so  high 
to  utilize  the  full  capacity  of  the  two  pipes  as  would  be  necessary 
to  discharge  itself  through  a  single  one  of  large  size. 

Iron  Pipe  Culverts.  During  recent  years  iron  pipe  has  been 
used  for  culverts  on  many  prominent  railroads,  and  may  be  used  on 
roads  in  sections  where  other  materials  are  unavailable. 

In  constructing  a  culvert  with  cast-iron  pipe  the  points  requiring 


309 


HIGHWAY  CONSTRUCTION 


particular  attention  are  (1)  tamping  the  soil  tightly  around  the  pipe 
to  prevent  the  water  from  forming  a  channel  along  the  outside,  and 
(2)  protecting  the  ends  by  suitable  head  walls  and,  when  necessary, 
laying  riprap  at  the  lower  end.  The  amount  of  masonry  required 
for  the  end  walls  depends  upon  the  relative  width  of  the  embankment 
and  the  number  of  sections  of  pipe  used.  For  example,  if  the  em- 
bankment is,  say,  40  feet  wide  at  the  base,  the  culvert  may  consist  of 
three  12-foot  lengths  of  pipe  and  a  light  end  wall  near  the  toe  of 
the  bank;  but  if  the  embankment  is,  say,  32  feet  wide,  the  culvert 
may  consist  of  two  12-foot  lengths  of  pipe  and  a  comparatively  heavy 
end  wall  well  back  from  the  toe  of  the  bank.  The  smaller  sizes  of 
pipe  usually  come  in  12-foot  lengths,  but  sometimes  a  few  6-foot 


Broken  Stones 
or  Bricks 


Fig.  20.    Section  of  Pipe  Culvert 

lengths  are  included  for  use  in  adjusting  the  length  of  the  culvert 
to  the  width  of  the  bank.     The  larger  sizes  are  generally  6  feet  long. 

EARTHWORK. 

The  term  "earthwork"  is  applied  to  all  the  operations  per- 
formed in  the  making  of  excavation  and  embankments.  In  its 
widest  sense  it  comprehends  work  in  rock  as  well  as  in  the  looser 
materials  of  the  earth's  crust. 

Balancing  Cuts  and  Fills.  In  the  construction  of  new  roads, 
the  formation  of  the  roadbed  consists  in  bringing  the  surface  of  the 
ground  to  the  adopted  grade  This  grade  should  be  established  so  as 


310 


HIGHWAY  CONSTRUCTION  45 

to  reduce  the  earthwork  to  the  least  possible  amount,  both  to  render 
the  cost  of  construction  low,  and  to  avoid  unnecessary  marring  the 
appearance  of  the  country  in  the  vicinity  of  the  road.  The  most 
desirable  position  of  the  grade  line  is  usually  that  which  makes  the 
amount  of  cutting  and  filling  equal  to  each  other,  for  any  surplus 
embankment  over  cutting  must  be  made  up  by  borrowing,  and  surplus 
cutting  must  be  wasted,  both  of  these  operations  involving  additional 
cost  for  labor  and  land. 

Inclination  of  Side  Slopes.  The  proper  inclination  for  the 
side  slopes  of  cutting  and  embankments  depends  upon  the  nature  of 
the  soil,  the  action  of  the  atmosphere  and  of  internal  moisture  upon 
it.  For  economy  the  inclination  should  be  as  steep  as  the  nature 
of  the  soil  will  permit. 

The  usual  slopes  in  cuttings  are: 

Solid  rock. 1  to  1 

Earth  and  Gravel 3^  to  1 

Clay .3  or  0  to  1 

Fine  sand 2  or  3  to  1 

The  slopes  of  embankment  are  usually  made  1^  to  1. 
Form  of  Side  Slopes.  The  natural,  strongest,  and  ultimate 
form  of  earth  slopes  is  a  concave  curve,  m  which  the  flattest  portion 
is  at  the  bottom.  This  form  is  very  rarely  given  to  the  slopes  in  con- 
structing them;  in  fact,  the  reverse  is  often  the  case,  the  slopes  being 
made  convex,  thus  saving  excavation  by  the  contractor  and  inviting 
slips. 

In  cuttings  exceeding  10  feet  in  depth  the  forming  of  concave 
•lopes  will  materially  aid  in  preventing  slips,  and  in  any  case  they  will 


Fig.  21.    Cross-Section  for  Embankment. 

reduce  the  amount  of  material  which  will  eventually  have  to  be  re- 
moved when  cleaning  up.  Straight  or  convex  slopes  will  continue 
to  slip  until  the  natural  form  is  attained. 

A  revetment  or  retaining  wall  at  the  base  of  a  slope  will  save 
excavation. 


311 


46  HIGHWAY  CONSTRUCTION 

In  excavations  of  considerable  depth,  and  particularly  in  soils 
liable  to  slips,  the  slope  may  be  formed  in  terraces,  the  horizontal 
offsets  or  benches  being  made  a  few  feet  in  width  with  a  ditch  on 
the  inner  side  to  receive  the  surface  water  from  the  portion  of  the 
side  slope  above  them.  These  benches  catch  and  retain  earth 
that  may  fall  from  the  slopes  above  them.  The  correct  forms  for  the 
slopes  of  embankment  and  excavation  are  shown  in  Figs.  21  and  22. 

Covering  of  Slopes.  It  is  not  usual  to  employ  any  artificial 
means  to  protect  the  surface  of  the  side  slopes  from  the  action  of  the 
weather;  but  it  is  a  precaution  which  in  the  end  will  save  much  labor 


Fig.  22.    Cross-Section  for  Excavation. 

and  expense  in  keeping  the  roadways  in  good  order.  The  simplest 
means  which  can  be  used  for  this  purpose  consists  in  covering  the 
slopes  with  good  sods,  or  else  with  a  layer  of  vegetable  mould  about 
four  inches  thick,  carefully  laid  and  sown  with  grass  seed.  These 
means  are  amply  sufficient  to  protect  the  side  slopes  from  injury 
when  they  are  not  exposed  to  any  other  cause  of  deterioration  than 
the  wash  of  the  rain  and  the  action  of  frost  on  the  ordinary  moisture 
retained  by  the  soil. 

A  covering  of  brushwood  or  a  thatch  of  straw  may  also  be  used 
with  good  effect;  but  from  their  perishable  nature  they  will  require 
frequent  renewal  and  repairs. 

Where  stone  is  abundant  a  small  wall  of  stone  laid  dry  may  be 
constructed  at  the  foot  of  the  slopes  to  prevent  any  wash  from  them 
being  carried  into  the  ditches. 

Shrinkage  of  Earthwork.  All  materials  when  excavated 
increase  in  bulk,  but  after  being  deposited  in  banks  subside  or  shrink 
(rock  excepted)  until  they  occupy  less  space  than  in  the  pit  from 
which  excavated. 

Rock,  on  the  other  hand,  increases  in  volume  by  being  broken 
up,  and  does  not  settle  again  into  less  than  its  original  bulk.  The 
.increase  may  be  taken  at  50  per  cent. 


312 


HIGHWAY  CONSTRUCTION  47 


The  shrinkage  in  the  different  materials  is  about  as  follows: 

.Gravel 8  per  cent 

Gravel  and  sand 9    ' 

Clay  and  clay  earths 10    " 

Loam  and  light  sandy  earths 12    ' 

Loose  vegetable  soil. . .  ., 15    "      " 

Puddled  clay 25    "       " 

Thus  an  excavation  of  loam  measuring  1,000  cubic  yards  will 
form  only  about  880  cubic  yards  of  embankment,  or  an  embankment 
of  1,000  cubic  yards  will  require  about  1,120  cubic  yards  measured 
in  excavation  to  make  it.  A  rock  excavation  measuring  1,000  yards 
will  make  from  1,500  to  1,700  cubic  yards  of  embankment,  depending 
upon  the  size  of  the  fragments. 

The  lineal  settlement  of  earth  embankments  will  be  about  in 
the  ratio  given  above;  therefore  either  the  contractor  should  be 
instructed  in  setting  his  poles  to  guide  him  as  to  the  height  of  grade 
on  an  earth  embankment  to  add  the  required  percentage  to  the  fill 
marked  on  the  stakes,  or  the  percentage  may  be  included  in  the 
fill  marked  on  the  stakes.  In  rock  embankments  this  is  not  necessary. 

Classification  of  Earthwork.  Excavation  is  usually  classi- 
fied under  the  heads  earth,  hardpan,  loose  rock,  and  solid  rock.  For 
each  of  these  classes  a  specific  price  is  usually  agreed  upon,  and  an 
extra  allowance  is  sometimes  made  when  the  haul  or  distance  to 
which  the  excavated  material  is  moved  exceeds  a  given  amount. 

The  characteristics  which  determine  the  classes  to  which  a  given 
material  belongs  are  usually  described  with  clearness  in  the  speci- 
fications, as: 

Earth  will  include  loam,  clay,  sand,  and  loose  gravel. 

Hardpan  will  include  cemented  gravel,  slate,  cobbles,  and  boul- 
ders containing  less  than  one  cubic  foot,  and  all  other  matters  of  an 
earthy  nature,  however  compact  they  may  be. 

Loose  rocjc  will  include  shale,  decomposed  rock,  boulders,  and 
detached  masses  of  rock  containing  not  less  than  three  cubic  feet, 
and  all  other  matters  of  a  rock  nature  which  may  be  loosened  with  a 
pick,  although  blasting  may  be  resorted  to  in  order  to  expedite  the 
work. " 

Solid  rock  will  include  all  rock  found  in  place  in  ledges  and 


813 


48  HIGHWAY  CONSTRUCTION 


masses,  or  boulders  measuring  more  than  three  cubic  feet,  and  which 
can  only  be  removed  by  blasting. 

Prosecution  of  Earthwork.  No  general  rule  can  be  laid 
down  for  the  exact  method  of  carrying  on  an  excavation  and  dis- 
posing of  the  excavated  material.  The  operation  in  each  case  can 
only  be  determined  by  the  requirements  of  the  contract,  character 
of  the  material,  magnitude  of  the  work,  length  of  haul,  etc. 

Formation  of  Embankments.  Where  embankments  are  to  be 
formed  of  less  than  two  feet  in  height,  all  stumps,  weeds,  etc.  should 
be  removed  from  the  space  to  be  occupied  by  the  embankment. 
For  embankments  exceeding  two  feet  in  height  stumps  need  only 
be  close  cut.  Weeds  and  brush,  however,  ought  to  be  removed  and 
if  the  surface  is  covered  with  grass  sod,  it  is  advisable  to  plow  a  fur- 
row at  the  toe  of  the  slope.  Where  a  cutting  passes  into  a  fill  all 
the  vegetable  matter  should  be  removed  from  the  surface  before 
placing  the  fill.  The  site  of  the  bank  should  be  carefully  examined 
and  all  deposits  of  soft,  compressible  matter  removed.  When  a  bank 
is  to  be  made  over  a  swamp  or  marsh,  the  site  should  be  thoroughly 
drained,  and  if  possible  the  fill  should  be  started  on  hard  bottom. 

Perfect  stability  is  the  object  aimed  at,  and  all  precautions  neces- 
sary to  this  end  should  be  taken.  Embankments  should  be  built  in 
successive  layers,  banks  two  feet  and  under  in  layers  from  six 
inches  to  one  foot,  heavier  banks  in  layers  2  and  3  feet  thick.  The 
horses  and  vehicles  conveying  the  materials  should  be  required  to 
pass  over  the  bank  for  the  purpose  of  consolidating  it,  and  care 
should  be  taken  to  have  the  layers  dip  towards  the  center.  Embank- 
ments first  built  up  in  the  center,  and  afterwards  widened  by  dump- 
ing the  earth  over  the  sides,  should  not  be  allowed. 

Embankments  on  Hillsides.  When  the  axis  of  the  road 
is  laid  out  on  the  side  slope  of  a  hill,  and  the  road  is  formed  partly 
by  excavating  and  partly  by  embanking,  the  usual  and  most  simple 
method  is  to  extend  out  the  embankment  gradually  along  the  whole 
line  of  the  excavation.  This  method  is  insecure;  the  excavated 
material  if  simply  deposited  on  the  natural  slope  is  liable  to  slip, 
and  no  pains  should  be  spared  to  give  it  a  secure  hold,  particularly 
at  the  toe  of  the  slope.  The  natural  surface  of  the  slope  should  be 
cut  into  steps  as  shown  in  Figs.  23  and  24.  The  dotted  line  A  B 


314 


•  j 


A  PECULIAR  EXAMPLE  OF  HIGHWAY  CONSTRUCTION 

By  means  of  the  truck  elevators  here  shown,  the  roadway  is  carried  over  the  steep  bluffs  of  the  Tal- 
isades  of  the  Hudson  at  Hoboken,  N.  J. 

Copyright,  1907,  by  Underwood  &  Underwood,  New  York 


HIGHWAY  CONSTRUCTION 


represents  the  natural  surface  of  the  ground,  C  E  B  the  excavation, 
and  ADC  the  embankment,  resting  on  steps  which  have  been  cut 
between  A  and  C.  The  best  position  for  these  steps  is  perpendicular 
to  the  axis  of  greatest  pressure.  If  A  D  is  inclined  at  the  angle  of 
repose  of  the  material,  the  steps  near  A  should  be  inclined  in  the 


Fig.  23.    Method  of  Construction  on  Hillsides. 

opposite  direction  to  A  D,  and  at  an  angle  of  nearly  90  degrees 
thereto,  while  the  steps  near  C  may  be  level.  If  stone  is  abundant, 
the  toe  of  the  slope  may  be  further  secured  by  a  dry  wall  of  stone. 
On  hillsides  of  great  inclination  the  above  method  of  construc- 
tion will  not  be  sufficiently  secure;  retaining  walls  of  stone  must 
be  substituted  for  the  side  slopes  of  both  the  excavations  and  em- 
bankments. These  walls  may  be  made  of  stone  laid  dry,  when  stone 


JL 


Fig.  24.    Hillside  Road  with  Retaining  and  Revetment  Walls. 

can  be  procured  in  blocks  of  sufficient  size  to  render  this  kind  of  con- 
struction of  sufficient  stability  to  resist  the  pressure  of  the  earth. 
When  the  stones  laid  dry  do  not  offer  this  security,  they  must  be  laid 
in  mortar.  The  wall  which  forms  the  slope  of  the  excavation  should 
be  carried  up  as  high  as  the  natural  surface  of  the  ground.  Unless 
the  material  is  such  that  the  slope  may  be  safely  formed  into  steps 
or  benches  as  shown  in  Fig.  23,  the  wall  that  sustains  the  embank- 
ment should  be  built  up  to  the  surface  of  the  roadway,  and  a  parapet 


315 


50  HIGHWAY  CONSTRUCTION 


wall  or  fence  raised  upon m  it,  to  protect  pedestrians  against  accident. 
(See  Fig.  24.) 

For  the  formula  for  calculating  the  dimensions  of  retaining  walls 
see  instruction  paper  on  Masonry  Construction. 

Roadways  on  Rock  Slopes.  On  rock  slopes  when  the  in- 
clination of  the  natural  surface  is  not  greater  than  one  perpendicular 
to  two  base,  the  road  may  be  constructed  partly  in  excavation  and 
partly  in  embankment  in  the  usual  manner,  or  by  cutting  the  face 
of  the  slope  into  horizontal  steps  with  vertical  faces,  and  building 
up  the  embankment  in  the  form  of  a  solid  stone  wall  in  horizontal 
courses,  laid  either  dry  or  in  mortar.  Care  is  required  in  proportion- 
ing the  steps,  as  all  attempts  to  lessen  the  quantity  of  excavation  by 
increasing  the  number  and  diminishing  the  width  of  the  steps  require 
additional  precautions  against  settlement  in  the  built-up  portion 
of  the  roadway. 

When  the  rock  slope  has  a  greater  inclination  than  1  : 2  the 
whole  of  the  roadway  should  be  in  excavation. 

In  some  localities  roads  have  been  constructed  along  the  face 
of  nearly  perpendicular  cliffs  on  timber  frameworks  consisting  of 
horizontal  beams,  firmly  fixed  at  one  end  by  being  let  into  holes 
drilled  in  the  rock,  the  other  end  being  Supported  by  an  inclined 
strut  resting  against  the  rock  in  a  shoulder  cut  to  receive  it.  There 
are  also  examples  of  similar  platforms  suspended  instead  of  being 
supported. 

Earth  Roads.  The  term  "earth  road"  is  applied  to  roads 
where  the  surface  consists  of  the  native  soil;  this  class  of  road  is  the 
most  common  and  cheapest  in  first  cost.  At  certain  seasons  of  the 
year  earth  roads  when  properly  cared  for  are  second  to  none,  but 
during  the  spring  and  wet  seasons  they  are  very  deficient  in-  the  im- 
portant requisite  of  hardness,  and  are  almost  impassable. 

For  the  construction  of  new  earth  roads,  all  the  principles  pre- 
viously discussed  relating  to  alignment,  grades,  drainage,  width,  etc., 
should  be  carefully,  followed.  The  crown  or  transverse  contour 
should  be  greater  than  in  stone  roads.  Twelve  inches  at  the  center 
in  25  feet  will  be  sufficient. 

Drainage  is  especially  important,  because  the  material  of  the 
road  is  more  susceptible  to  the  action  of  water,  and  more  easily 


316 


HIGHWAY  CONSTRUCTION 


Bl 


destroyed  by  it  than  are  the  materials  used  in  the  construction  of  the 
better  class  of  roads.  When  water  is  allowed  to  stand  upon  the 
road,  the  earth  is  softened,  the  wagon  wheels  penetrate  it  and  the 
horses'  feet  mix  and  kneed  it  until  it  becomes  impassable  mud.  The 
action  of  frost  is  also  apt  to  be  more  disastrous  upon  the  more  per- 
meable surface  of  the  earth  road,  having  the  effect  of  swelling  and 
heaving  the  roadwray  and  throwing  its  surface  out  of  shape.  It  mav 


Fig.  25.    Bush  Hooks. 

in  fact  be  said  that  the  whole  problem  of  the  improvement  and 
maintenance  of  ordinary  country  roads  is  one  of  drainage. 

In  the  preparation  of  the  wheelway  all  stumps,  brush,  vegetable 
matter,  rocks  and  boulders  should  be  removed  from  the  surface  and 
the  resulting  holes  filled  in  with  clean  earth.  The  roadbed  having 


Fig.  26.    Axe  Mattock. 


Fig.  27.     Bush  Mattock. 


been  brought  to  the  required  grade  and  crown  should  be  thoroughly 
rolled,  all  inequalities  appearing  during  the  rolling  should  be  filled 
up  and  re-rolled. 

Care  of  Earth  Roads.  If  the  surface  of  the  roadway  is  prop- 
erly formed  and  kept  smooth,  the  water  will  be  shed  into  the  side 
ditches  and  do  comparatively  little  harm;  but  if  it  remains  upon  the 
surface,  it  will  be  absorbed  and  convert  the  road  into  mud.  All 
ruts  and  depressions  should  be  filled  up  as  soon  as  they  appear. 
Repairs  should  be  attended  to  particularly  in  the  spring.  At  this 
season  a  judicious  use  of  a  road  machine  and  rollers  will  make  a 


317 


52  HIGHWAY  CONSTRUCTION 


smooth  road.  In  summer  when  the  surface  gets  roughed  up  it  can 
be  improved  by  running  a  harrow  over  it;  if  the  surface  is  a  little 
muddy  this  treatment  will  hasten  the  drying. 

During  the  fall  the  surface  should  be  repaired,  with  special 
reference  to  putting  it  in  shape  to  withstand  the  ravages  of  winter. 
Saucer-like  depressions  and  ruts  should  be  filled  up  with  clean  earth 
similar  to  that  of  the  roadbed  and  tamped  into  place. 

The  side  ditches  should  be  examined  in  the  fall  to  see  that  they 
are  free  from  dead  weeds  and  grass,  and  late  in  winter  they  should 
be  examined  again  to  see  that  they  are  not  clogged.  The  mouths  of 
culverts  should  be  cleaned  of  rubbish  and  the  outlet  of  tile  drains 
opened.  Attention  to  the  side  ditches  will  prevent  overflow,  and 
washing  of  the  roadway,  and  will  also  prevent  the  formation  of  ponds 
at  the  roadside  and  the  consequent  saturation  of  the  roadbed., 

Holes  and  ruts  should  not  be  filled  with  stone,  bricks,  gravel 
or  other  material  harder  than  the  earth  of  the  roadway  as  the  hard 
material  will  not  wear  uniform  with  the  rest  of  the  road,  but  produce 
bumps  and  ridges,  and  usually  result  in  making  two  holes,  each 
larger  than  the  original  one.  It  is  bad  practice  to  cut  a  gutter  from 
a  hole  to  drain  it  to  the  side  of  the  road.  Filling  is  the  proper  course, 
whether  the  hole  is  dry  or  contains  mud. 

In  the  maintenance  of  clay  roads  neither  sods  nor  turf  should 
be  used  to  fill  holes  or  ruts;  for,  though  at  first  deceptively  tough, 
they  soon  decay  and  form  the  softest  mud.  Neither  should  the  ruts 
be  filled  with  field  stones;  they  will  not  wear  uniformly  with  the  rest 
of  the  road,  but  will  produce  hard  ridges. 

Trees  and  close  hedges  should  not  be  allowed  within  200  feet 
of  a  clay  road.  It  requires  all  the  sun  and  wind  possible  to  keep  its 
surface  in  a  dry  and  hard  condition. 

Sand  Roads.  The  aim  in  the  improvement  of  sand  roads  is  to 
have  the  wheelway  as  narrow  and  well  defined  as  possible,  so  as  to 
have  all  the  vehicles  run  in  the  same  track.  An  abundant  growth 
of  vegetation  should  be  encouraged  on  each  side  of  the  wheelway, 
for  by  this  means  the  shearing  of  the  sand  is,  in  a  great  measure, 
avoided.  Ditching  beyond  a  slight  depth  to  carry  away  the  rain 
water  is  not  desirable,  for  it  tends  to  hasten  the  drying  of  the  sands 
which  is  to  be  avoided.  Where  possible  the  roads  should  be  over- 


318 


HIGHWAY  CONSTRUCTION 


58 


hung  with  trees,  the  leaves  and  twigs  of  which  catching  on  the 
wheelway  will  serve  still  further  to  diminish  the  effect  of  the  wheels 
in  moving  the  sands  about.  If  clay  can  be  obtained,  a  coating  6 
inches  thick  will  be  found  a  most  effective  and  economical  improve- 
ment. A  coating  of  4  inches  of  loose  straw  will,  after  a  few  days' 
travel,  grind  into  the  sand  and  become  as  hard  and  as  firm  as  a 
dry  clay  road. 

The  maintaining  of  smooth  surfaces  on  all  classes  of  earth  roads 
will  be  greatly  assisted  and  cheapened  by  the  frequent  use  of  a  roller 
(either  steam  or  horse)  and  any  one  of  the  various  forms  of  road 
grading  and  scraping  machines.  In  repairing  an  earth  road  the 
plough  should  not  be  used.  It  breaks  up  the  surface  which  has 
been  compacted  by  time  and  travel. 

TOOLS  FOR  GRADING. 

Picks  are  made  of  various  styles,  according  to  the  class  of 
material  in  which  they  are  to  be  used.  Fig.  28  shows  the  form 


Fig.  29.    Clay  Pick. 

usually  employed  in  street  work.     Fig.  29  shows  the  form  generally 
used  for  clay  or  gravel  excavation. 

The  eye  of  the  pick  is  generally  formed  of  wrought  iron,  pointed 
with  steel.     The  weight  of  picks  ranges  from  4  to  9  Ib. 


Fig.  30.     Shovels. 

Shovels  are  made  in  two  forms,  square  and  round  pointed, 
usually  of  pressed  steel. 

Ploughs  are  extensively  employed  in  grading,  special  forms 
being  manufactured  for  the  purpose.  They  are  known  as  "grading 
ploughs,"  "  road  ploughs/'  "  township  ploughs,"  etc.  They  vary 


319 


54 


HIGHWAY  CONSTRUCTION 


in  form  according  to  the  kind  of  work  they  are  intended  for,  viz. : 
loosening  earth,  gravel,  hardpan,  and  some  of  the  softer  rocks. 

These  ploughs  are  made  of  great  strength,  selected  white  oak, 
rock  elm,  wrought  steel  and  iron  being  generally  used  in  their  con- 
struction. The  cost  of  operating  ploughs  ranges  from  2  to  5  cents 
per  cubic  yard,  depending  upon  the  compactness  of  the  soil.  The 
quantity  of  material  loosened  will  vary  from  2  to  5  cubic  yards  per 
hour. 

Fig.  31  shows  the  form  usually  adopted  for  loosening  earth. 
This  plough  does  not  turn  the  soil,  but  cuts  a  furrow  about  10 


Fig.  31.    Grading  Plow. 


inches  wide  and  of  a  depth  adjustable  up  to  11  inches. 

In  light  soil  the  ploughs  are  operated  by  two  or  four  horses;  in 
heavy  soils  as  many  as  eight  are  employed.  Grading  ploughs  vary 
in  weight  from  100  to  325  Ib. 


Fig.  32.    Hardpan  Plow. 


Fig.  32  illustrates  a  plough  specially  designed  for  tearing  up 
macadam,  gravel,  or  similar  material.  The  point  is  a  straight  bar 
of  cast  steel  drawn  down  to  a  point,  and  can  be  easily  repaired. 


320 


HIGHWAY  CONSTRUCTION 


55 


Scrapers  are  generally  used  to  move  the  material  loosened  by 
ploughing;  they  are  made  of  either  iron  or  steel,  and  in  a  variety 
of  form,  and  are  known  by  various  names,  as  "drag,"  "buck," 
"  pole,"  and  "  wheeled".  The  drag  scrapers  are  usually  employed 
on  short  hauls,  the  wheeled  on  long  hauls.  Fig.  33  illustrates  the 
usual  form  of  drag  scrapers. 

Drag  scrapers  are  made  in  three  sizes.  The  smallest,  for  one 
horse,  has  a  capacity  of  3  cubic  feet;  the  others,  for  two  horses, 


Fig.  33.    Drag  Scraper. 

have  a  capacity  of  5  to  1\  cubic  feet.  The  smallest  weighs  about 
90  lb.,  and  the  larger  ones  from  94  to  102  Ib. 

Buck  scrapers  are  made  in  two  sizes — two-horses,  carrying  1\ 
cubic  feet;  four-horses,  12  cubic  feet. 

Pole  scraper,  Fig.  34,  is  designed  for  use  in  making  and  leveling 
earth  roads  and  for  cutting  and  cleaning  ditches;  it  is  also  well 


Fig.  34.    Pole  Scraper. 


adapted  for  moving  earth  short  distances  at  a  minimum  cost. 

Wheeled  scrapers  consist  of  a  metal  box,  usually  steel,  mounted 
~on   wheels,    and   furnished    with    levers  for   raising,   lowering,  and 


321 


56 


HIGHWAY  CONSTRUCTION 


dumping.  They  are  operated  in  the  same  manner  as  drag  scrapers, 
except  that  all  the  movements  are  made  by  means  of  the  levers,  and 
without  stopping  the  team.  By  their  use  the  excessive  resistance  to 


Fig.  35.    Wheeled  Scraper. 

traction  of  the  drag  scraper  is  avoided.  Various  sizes  are  made, 
ranging  in  capacity  from  10  to  17  cubic  feet.  In  weight  they  range 
from  350  to  700  Ib. 

Wheelbarrows.  The  wheelbarrow  shown  in  Fig.  36  is  con- 
structed of  wood  and  is  the  most  commonly  employed  for  earth- 
work. Its  capacity  ranges  from  2  to  2|  cubic  feet.  Weight  about 
50  Ib. 

The  barrow,  Fig.  37,  has  a  pressed-steel  tray,  oak  frame,  and 
steel  wheel,  and  will  be  found  more  durable  in  the  maintenance 


Fig.  36.    Wooden  Barrow. 


department  than  the  all  wood  barrow.     Capacity  from  3i  to  5  cubic 
feet,  depending  on  size  of  tray. 

The  barrow,  Fig.  38,  is  constructed   with  tubular  iron   frames 
and  steel   tray,    and  is  adaptable  to   the    heaviest  work,  such  as 


322 


HIGHWAY  CONSTRUCTION 


moving  heavy  broken  stone,  etc.,  or  it  may  be  employed  with  ad- 
vantage in  the  cleaning  department.  Capacity  from  3  to  4  cubic 
feet.  Weight  from  70  to  82  Ib. 


Fig.  37.    Steel  Tray  Barrow. 

The  maximum  distance  to  which  earth  can  be  moved  economic- 
ally in  barrows  is  about  200  feet.  The  wheeling  should  be  per- 
formed upon  planks,  whose  steepest  inclination  should  not  exceed  1 
in  12.  The  force  required  to  move  a  barrow  on  a  plank  is  about  aV 
part  of  the  weight;  on  hard  dry  earth,  about  yT  part  of  the  weight. 


Fig.  38.    Metal  Barrow. 

The  time  occupied  in  loading  a  barrow  will  vary  with  the 
character  of  the  material  and  the  proportion  of  wheelers  to  shovel- 
lers. Approximately,  a  shoveller  takes  about  as  long  to  fill  a  barrow 
with  earth  as  a  wheeler  takes  to  wheel  a  full  barrow  a  distance  of 
about  100  or  120  feet  on  a  horizontal  plank  and  return  with  the 
empty  barrow. 

Carts.  The  cart  usually  employed  for  hauling  earth,  etc.,  is 
shown  in  Fig.  39.  The  average  capacity  is  22  cubic  feet,  and  the 
average  weight  is  800  Ib.  These  carts  are  usually  furnished  with 
broad  tires,  and  the  body  is  so  balanced  that  the  load  is  evenly 
divided  about  the  axle. 


883 


58 


HIGHWAY  CONSTRUCTION 


The  time  required  to  load  a  cart  varies  with  the  material.  One 
shoveller  will  require  about  as  follows:  Clay,  seven  minutes;  loam, 
six  minutes;  sand,  five  minutes. 


Fig.  3i).    Earth  Wagon. 

Dump  Cars.  These  cars  are  made  to  dump  in  several  different 
ways,  viz.,  single  or  double  side,  single  or  double  end,  and  rotary 
or  universal  dumpers. 

Dump  cars  may  be  operated  singly  or  in  trains,  as  the  magni- 
tude of  the  work  miy  demand.  They  may  be  moved  by  horses  or 


Fig.  40.    Dump  Cart. 

small  locomotives.     They  are  made  in  various  sizes,  depending  upon 
the  gauge  of  the  track  on  which  they  are  run.     A  common  gauge  is 


324 


HIGHWAY  CONSTRUCTION  59 

20  inches,  but  it  varies  from  that  up  to  the  standard  railroad  gauge 
of  56  ;j  inches. 

Dump  Wagons.  (Fig.  40.)  The  use  of  these  wagons  for  mov- 
ing excavated  earth,  etc.,  and  for  transporting  materials  such  as  sand, 
gravel,  etc.,  materially  shortens  the  time  required  for  unloading  the 
ordinary  form  of  contractor's  wagon;  having  no  reach  or  pole  con- 
necting the  rear  axle  with  the  center  bearing  of  the  front  axle,  they 
may  be  cramped  short  and  the  load  deposited  just  where  required. 
They  are  operated  by  the  driver,  and  the  capacity  ranges  from  35 
to  45  cubic  feet. 

Mechanical  Graders  are  used  extensively  in  the  making  and 
maintaining  of  earth  roads.  They  excavate  and  move  earth  more 
expeditiously  and  economically  than  can  be  done  by  hand;  they  are 
called  by  various  names,  such  as  "road  machines,"  "graders," 
"road  hones,"  etc.  Their  general  form  is  shown  in  Fig.  41. 

Briefly  described,  they  consist  of  a  large  blade  made  entirely 
of  steel  or  of  iron,  or  wood  shod  with  steel,  which  is  so  arranged  by 
mechanism  attached  to  the  frame  from  which  it  is  suspended  that  it 
can  be  adjusted  and  fixed  in  any  direction  by  the  operator.  In  their 
action  they  combine  the  work  of  excavating  and  transporting  the 


Fig.  41.    Mechanical  Grader. 

earth.  They  have  been  chiefly  employed  in  the  forming  and  main- 
tenance of  earth  roads,  but  may  be  also  advantageously  used  in  pre- 
paring the  subgrade  surface  of  roads  for  the  reception  of  broken 
stone  or  other  improved  covering. 

A  large   variety   of  such   machines  are  on  the  market.     The 
"New  Era"  grader  excavates  the  material  from  side  ditches,  and 


HIGHWAY  CONSTRUCTION  61 


wagons  in  the  same  time,  and  that  the  cost  of  this  handling  is  from 
1 '  to  2V  cents  per  cubic  yard. 

Points  to  be  Considered  in  Selecting  a  Road  Machine.  In 
the  selection  of  a  road  machine  the  following  points  should  he  care- 
fully considered: 

(1)  Thoroughness  and  simplicity  of  its  mechanical  construction. 

(2)  Material  and  workmanship  used  in  its  construction. 

(3)  Ease  of  operation. 

(4)  Lightness  of  draft. 

(5)  Adaptability  for  doing  general  road-work,  ditching,  etc. 

(6)  Safety  to  the  operator. 

Care  of  Road  Machines.  The  road  machine  when  not  in  use 
should  be  stored  in  a  dry  house  and  thoroughly  cleaned,  its  blade 
brushed  clean  from  all  accumulations  of  mud,  wiped  thoroughly  dry, 
and  well  covered  with  grease  or  crude  oil.  The  axles,  journals,  and 
wearing  parts  should  be  kept  well  oiled  when  in  use,  and  an  extra 
blade  should  be  kept  on  hand  to  avoid  stopping  the  machine  while 
the  dulled  one  is  being  sharpened. 

Surface  Graders.  The  surface  grader,  Fig.  42,  is  used  for  re- 
moving earth  previously  loosened  by  a  plough.  It  is  operated  by 
one  horse.  The  load  may  be  retained  and  carried  a  considerable 


Fig.  42.    Surface  Grader. 

distance,  or  it  may  be  spread  gradually  as  the  operator  desires.     It 
is  also  employed  to  level  off  and  trim  the  surface  after  scrapers. 

The  blade  is  of  steel,  J-inch  thick,  15  inches  wide,  and  30 
inches  long.  The  beam  and  other  parts  are  of  oak  and  iron. 
Weight  about  60  Ib. 


327 


62 


HIGHWAY  CONSTRUCTION 


The  road  leveller,  Fig.  43,  is  used  for  trimming  and  smoothing 
the  surface  of  earth  roads.  It  is  largely  employed  in  the  Spring 
when  the  frost  leaves  the  ground. 


Fig.  43.    Road  Leveller. 


N0.3.    NO.  4.    NO.  5. 


No.S. 


No.  6. 


No.l.  No  7 

Fig.  44.    Draining  Tools. 

The  blade  is  of  steel,  i-inch  thick  by  4  inches  by  72  inches,  and 
is  provided  with  a  seat  for  the  driver.  It  is  operated  by  a  team  of 
horses.  Weight  about  150  Ib. 


328 


HIGHWAY  CONSTRUCTION 


63 


Draining=tools.  The  tools  employed  for  digging  the  ditches 
and  shaping  the  bottom  to  fit  the  drain  tiles  are  shown  in  Fig.  44. 
They  are  convenient  to  use,  and  expedite  the  work  by  avoiding 
unnecessary  excavation. 

The  tools  are  used  as  follows:  Nos.  3,  4  and  5  are  used  for 
digging  the  ditches;  Nos.  6  and  7  for  cleaning  and  rounding  the 


Fig.  45.    Reversible  Roller. 

bottom  of  the  ditch  for  round  tile.  No.  2  is  used  for  shoveling  out 
loose  earth  and  levelling  the  bottom  of  the  ditch;  No.  1  is  used  for 
the  same  purpose  when  the  ditch  is  intended  for  "sole  "  tile. 


Fig.  46.    Watering  Cart. 

Horse  Rollers.  There  is  a  variety  of  horse  rollers  on  the 
market.  Fig.  45  shows  the  general  form.  Each  consists  essentially 
of  a  hollow  cast-iron  cylinder  4  to  5  feet  long,  5  to  6  feet  in 


64  HIGHWAY  CONSTRUCTION 


diameter,  and  weighing  from  3  to  6  tons.  Some  forms  are  provided 
with  boxes  in  which  •  stone  or  iron  may  be  placed  to  increase  the 
weight,  and  some  have  closed  ends  and  may  be  filled  with  water  or 
sand. 

Sprinkling-carts.  Fig.  46  shows  a  convenient  form  of  sprink- 
ling cart  for  suburban  streets  and  country  roads.  Capacity  about 
150  gallons. 

ROAD  COVERINGS. 

Road  coverings  consist  of  some  foreign  material  as  gravel, 
broken  stone,  clay,  etc.,  placed  on  the  surface  of  the  earth  road. 
The  object  of  this  covering,  whatever  its  nature,  is  (1)  to  protect  the 
natural  soil  from  the  effect  of  weather  and  travel,  and  (2)  to  furnish 
a  smooth  surface  on  which  the  resistance  to  traction  will  be  reduced 
to  the  least  possible  amount,  and  over  which  vehicles  may  pass  with 
safety  and  expedition  at  all  seasons  of  the  year.  .  Where  an  artificial 
covering  is  employed,  the  wheel  loads  coming  upon  its  surface  are 
distributed  over  a  greater  area  of  the  roadbed  than  if  the  loads 
come  directly  upon  the  earth  itself.  The  loads  are  not  sustained  by 
the  covering  as  a  rigid  structure,  but  are  transferred  through  it  to 
the  roadbed,  which  must  support  both  the  weight  of  the  covering 
and  the  load  coming  upon  it. 

Gravel  Roads.  Gravel  is  an  accumulation  of  small  more  or 
less  rounded  stones  which  usually  vary  from  the  size  of 'a  small  pea 
to  a  walnut.  It  is  often  intermixed  with  other  substances,  such  as 
sand,  clay,  loam,  etc.,  from  each  of  which  it  derives  a  distinctive 
name.  In  selecting  gravel  for  road  purposes  the  chief  quality  to  be 
sought  for  is  the  property  of  binding. 

Gravel  in  general  is  unserviceable  for  roadmaking.  This  is 
due  mainly  to  the  fact  that  the  surface  of  the  pebbles  is  smooth,  so 
that  they  will  not  bind  together  in  the  manner  of  broken  stone. 
There  is  also  an  absence  of  dust  or  other  material  to  serve  as  a 
binder,  and  even  if  such  binding  material  is  furnished  it  is  difficult 
to  effectively  hold  the  rounded  and  polished  surface  of  the  pebbles 
together. 

In  certain  deposits  of  gravel,  particularly  where  the  pebbly 
matter  is  to  a  greater  or  less  extent  composed  of  limestone,  a  con- 
siderable amount  of  iron  oxide  has  been  gathered  in  the  mass. 


330 


HIGHWAY  CONSTRUCTION 


This  effect  is  due  to  the  tendency  of  water  which  contains  iron  to 
lay  down  that  substance  and  to  take  lime  in  its  place  when  the 
opportunity  for  so  doing  occurs.  Such  gravels  are  termed  ferru- 
ginous. They  are  commonly  found  in  a  somewhat  cemented  state, 
and  when  broken  up  and  placed  upon  roads  they  again  cement,  even 
more  firmly  than  in  the  original  state,  often  forming  a  roadway  of 
very  good  quality. 

When  no  gravel  but  that  found  in  rivers  or  on  the  seashore  can 
be  obtained,  one-half  of  the  stone  should  be  broken  and  mixed  with 
the  other  half;  to  the  stone  so  mixed  a  small  quantity  of  clay  or 
loam,  about  one-eighth  of  the  bulk  of  the  gravel,  must  be  added: 
an  excess  is  injurious.  Sand  is  unsuitable.  It  prevents  packing  in 
proportion  to  the  amount  added. 

Preparing  the  Gravel.  Pit  gravel  usually  contains  too  much 
earth,  and  should  be  screened  before  being  used.  Two  sieves  should 
be  provided,  one  with  meshes  of  one  and  one-half  inches,  so  that  all 
pebbles  above  that  size  may  be  rejected,  the  other  with  meshes  of 
three  quarters  of  an  inch,  and  the  material  which  passes  through  it 
should  be  thrown  away.  The  expense  of  screening  will  be  more 
than  repaid  by  the  superior  condition  of  the  road  formed  by  the 
cleaned  material,  and  by  the  diminution  of  labor  in  keeping  it  in 
order.  The  pebbles  larger  than  one  and  a  half  inches  may  be 
broken  to  that  size  and  mixed  with  clean  material. 

Laying  the  Gravel.  On  the  roadbed  properly  prepared  a  layer 
of  the  prepared  gravel  four  inches  thick  is  uniformly  spread  over  the 
whole  width,  then  compacted  with  a  roller  weighing  not  less  than 
two  tons,  and  having  a  length  of  not  less  than  thirty  inches.  The 
rolling  must  be  continued  until  the  pebbles  cease  to  rise  or  creep  in 
front  of  the  roller.  The  surface  must  be  moistened  by  sprinkling 
in  advance  of  the  roller,  but  too  much  water  must  not  be  used. 
Successive  layers  follow,  each  being  treated  in  the  above  described 
manner  until  the  requisite  depth  and  form  has  been  attained. 

The  gravel  in  the  bottom  layer  must  be  no  larger  than  that  in 
the  top  layer;  it  must  be  uniformly  mixed,  large  and  small  together, 
for  if  not,  the  vibration  of  the  traffic  and  the  action  of  frost  will 
cause  the  larger  pebbles  to  rise  to  the  surface  and  the  smaller  ones 
to  descend,  and  the  road  will  never  be  smooth  or  firm. 


331 


HIGHWAY  CONSTRUCTION 


The  pebbles  in  a  gravel  road  are  simply  imbedded  in  a  paste 
and  can  be  easily  displaced.  It  is  for  this  reason,  among  others, 
that  such  roads  are  subject  to  internal  destruction. 

The  binding  power  of  clay  depends  in  a  large  measure  upon 
the  state  of  the  weather.  During  rainy  periods  a  gravel  road  be- 
comes soft  and  muddy,  while  in  very  dry  weather  the  clay  will  con- 
tract and  crack,  thus  releasing  the  pebbles,  and  giving  a  loose 
surface.  The  most  favorable  conditions  are  obtained  in  moderately 
damp  or  dry  weather,  during  which  a  gravel  road  offers  several 
advantages  for  light  traffic,  the  character  of  the  drainage,  etc., 
largely  determining  durability,  cost,  maintenance,  etc. 

Repair.  Gravel  roads  constructed  as  above  described  will 
need  but  little  repairs  for  some  years,  but  daily  attention  is  required 
to  make  these.  A  garden  rake  should  be  kept  at  hand  to  draw 
any  loose  gravel  into  the  wheel  tracks,  and  for  filling  any  depres- 
sions that  may  occur. 

In  making  repairs,  it  is  best  to  apply  a  small  quantity  of  gravel 
at  a  time,  unless  it  is  a  spot  which  has  actually  cut  through.  Two 
inches  of  gravel  at  once  is  more  profitable  than  a  larger  amount. 
Where  a  thick  coating  is  applied  at  once  it  does  not  all  pack,  and  if, 
after  the  surface  is  solid,  a  cut  be  made,  loose  gravel  will  be  found; 
this  holds  water  and  makes  the  road  heave  and  become  spouty 
under  the  action  of  frost.  It  will  cost  no  more  to  apply  six  inches 
of  gravel  at  three  different  times  than  to  do  it  at  once. 

At  every  one-eighth  of  a  mile  a  few  cubic  yards  of  gravel 
should  be  stored  to  be  used  in  filling  depressions  and  ruts  as  fast  as 
they  appear,  and  there  should  be  at  least  one  laborer  to  every  five 
miles  of  road. 

Broken  Stone  Roads.  Broken  stone  roads  are  formed  by  pla- 
cing small  angular  fragments  of  stone  on  the  surface  of  the  earth 
roadbed  and  compacting  into  a  solid  mass  by  rolling.  This  class 
of  road  covering  is  generally  called  a  Macadam  or  Telford  road 
from  the  name  of  the  two  men  who  first  introduced  this  type  into 
England. 

The  name  of  Telford  is  associated  with  a  rough  stone  founda- 
tion, which  he  did  not  always  use,  but  which  closely  resembled  that 
which  had  been  previously  used  in  France.  Macadam  disregarded 


HIGHWAY  CONSTRUCTION  67 

this  foundation,  contending  that  the  subsoil,  however  bad,  would 
carry  any  weight  if  made  dry  by  drainage  and  kept  dry  by  an  im- 
pervious covering.  The  names  of  both  have  ever  since  been 
associated  witli  the  class  of  road  which  each  favored,  as  well  as  with 
roads  on  which  all  their  precepts  have  been  disregarded. 

Quality  of  Stones.  The  materials  used  for  broken-stone  pave- 
ments must  of  necessity  vary  very  much  according  to  the  locality. 
Owing  to  the  cost  of  haulage,  local  stone  must  generally  be  used, 
especially  if  the  traffic  be  only  moderate.  If,  however,  the  traffic  is 
heavy,  it  will  sometimes  be  found  better  and  more  economical  to 
obtain  a  superior  material,  even  at  a  higher  cost,  than  the  local 
stone;  and  in  cases  where  the  traffic  is  very  great,  the  best  material 
that  can  be  obtained  is  the  most  economical. 

The  qualities  required  in  a  good  road  stone  are  hardness  and 
and  toughness  and  ability  to  resist  the  disintegrating  action  of  the 
weather.  These  qualities  are  seldom  found  together  in  the  same 
stone.  Igneous  and  siliceous  rocks,  although  frequently  hard  and 
tough,  do  not  consolidate  so  well  nor  so  quick  as  limestone,  owing 
to  the  sandy  detritus  formed  by  the  two  first  having  no  cohesion, 
whilst  the  limestone  has  a  detritus  which  acts  like  mortar  in  binding 
the  stones  together. 

A  stone  of  good  binding  nature  will  frequently  wear  much 
better  than  one  without,  although  it  is  not  so  hard.  A  limestone 
road  well  made  and  of  good  cross-section  will  be  more  impervious 
than  any  other,  owing  to  this  cause,  and  will  not  disintegrate  so 
soon  in  dry  weather,  owing  partly  to  this  and  partly  to  the  well- 
known  quality  which  all  limestone  has  of  absorbing  moisture  from 
the  atmosphere.  Mere  hardness  without  toughness  is  not  of  much 
use,  as  a  stone  may  be  very  hard  but  so  brittle  as  to  be  crushed  to 
powder  under  a  heavy  load,  while  a  stone  not  so  hard  but  having  a 
greater  degree  of  toughness  will  be  uninjured. 

By  a  stone  of  good  binding  quality  is  meant  one  that,  when 
moistened  by  water  and  subjected  to  the  pressure  of  loaded  wheels 
or  rollers,  will  bind  or  cement  together.  This  quality  is  possessed  to 
a  greater  or  less  extent  by  nearly  all  rocks  when  in  a  state  of  dis- 
integration. The  binding  is  caused  by  the  action  of  water  upon  the 
chemical  constituents  of  the  stone  contained  in  the  detritus  produced 


HIGHWAY  CONSTRUCTION 


by  crushing  the  stone,  and  by  the  friction  of  the  fragments  on  each 
other  while  being  compacted;  its  strength  varies  with  the  different 
species  of  rock,  but  it  exists  in  some  measure  with  them  all,  being 
greatest  with  limestone  and  least  with  gneiss. 

The  essential  condition  of  the  stone  to  produce  this  binding 
effect  is  that  it  bj  sound.  No  decayed  stone  retains  the  property  of 
binding,  though  in  some  few  cases,  where  the  material  contains  iron 
oxides,  it  may,  by  the  cementing  property  of  the  oxide,  undergo  a 
certain  binding. 

A  stone  for  a  road  surface  should  be  as  little  absorptive  of 
moisture  as  possible  in  order  that  it  may  not  suffer  injury  from  the 
action  of  frost.  Many  limestones  are  objectionable  on  this  account. 

The  stone  used  should  be  uniform  in  quality,  otherwise  it  will 
wear  unevenly,  and  depressions  will  appear  where  the  softer  material 
has  been  used. 

As  the  under  parts  of  the  road  covering  are  not  subject  to  the 
wear  of  traffic,  and  have  only  the  weight  of  loads  to  sustain,  it  is 
not  necessary  that  the  stone  of  the  lower  layer  be  so  hard  or  so 
tough  as  the  stone  for  the  surface,  hence  it  is  frequently  possible  by 
using  an  inferior  stone  for  that  portion  of  the  work,  to  greatly  reduce 
the  cost  of  construction. 

Size  of  Stones.  The  stone  should  be  broken  into  fragments 
as  nearly  cubical  as  possible.  The  size  of  the  cubes  will  depend 
upon  the  character  of  the  rock.  If  it  be  granite  or  trap,  they  should 
not  exceed  1^  inches  in  their  greatest  dimensions;  if  limestone,  they 
should  not  exceed  2  inches. 

The  smaller  the  stones  the  less  the  percentage  of  voids.  Small 
stones  compact  sooner,  require  less  binding,  and  make  a  smoother 
surface  than  large  ones,  but  the  size  of  the  stone  for  any  particular 
section  of  a  road  must  be  determined  to  a  certain  extent  by  the 
amount  of  traffic  which  it  will  have  to  bear  and  the  character  of  the 
rock  used. 

It  is  not  necessary  nor  is  it  advisable  that  the  stone  should  be 
all  of  the  same  size;  they  may  be  of  all  sizes  under  the  maximum. 
In  this  condition  the  smaller  stones  fill  the  voids  between  the  larger 
and  less  binding  is  required. 

Thickness  of  the  Broken  Stone.     The   offices  of  the  broken 


HIGHWAY  CONSTRUCTION 


stone  are  to  endure  friction  and  to  shed  water;  its  thickness  must 
be  regulated  by  the  quality  of  the  stone,  the  amount  of  traffic,  and 
nature  of  the  natural  soil  bed.  Under  heavy  traffic  it  is  advisable 
to  make  the  thickness  greater  than  for  light  traffic,  in  order  to  pro- 
vide for  wear  and  lessen  the  cost  of  renewals. 

When  the  roadbed  is  firm,  well  drained,  and  not  likely  to  be 
affected  by  ground  water,  it  will  always  afford  a  firm  foundation 
for  the  broken  stone,  the  thickness  of  which  may  be  made  the  mini- 
mum for  good  construction.  This  thickness  is  four  inches.  When 
this  thickness  is  employed  the  stone  must  be  of  exceptionally  fine 
quality  and  the  road  must  be  maintained  by  the  "  continuous  " 
method.  With  heavy  traffic  the  thickness  should  be  increased  over 
the  minimum  a  certain  amount,  say  2  inches,  to  provide  for  wear. 
Where  the  foundation  is  unstable  and  there  is  a  tendency  on  the 
part  of  the  loads  to  break  through  the  covering,  the  thickness  of 
the  stone  must  be  made  the  maximum,  which  is  12  inches.  In  such 
a  case  it  may  be  advisable  to  employ  a  Telford  foundation.  Where 
the  covering  exceeds  six  inches  in  thickness,  the  excess  may  be 
composed  of  gravel,  sand  or  ledge  stone,  the  choice  depending 
entirely  on  the  cost,  for  all  are  equally  effective. 

Foundation.  The  preparation  of  the  natural  soil  over  which 
the  road  is  to  be  constructed,  to  enable  it  to  sustain  the  superstruc- 
ture and  the  weights  brought  upon  it,  requires  the  observance  of 
certain  precautions  the  neglect  of  which  will  sooner  or  later  result 
in  the  deterioration  or  possible  destruction  of  the  road  covering. 
These  precautions  vary  with  the  character  of  the  soil. 

Soils  of  a  siliceous  and  calcareous  nature  do  not  present  any 
great  difficulty,  as  their  porous  nature  generally  affords  good  natural 
drainage  which  secures  a  dry  foundation.  Their  surface,  however, 
requires  to  be  compacted;  this"  is  effected  by  rolling. 

The  rolling  should  be  carried  out  in  dry  weather,  and  any  de- 
pressions caused  by  the  passage  of  the  roller  should  be  filled  with 
the  same  class  of  material  as  the  surrounding  soil.  The  rolling 
must  be  repeated  until  a  uniform  and  solid  bed  is  obtained. 

The  argillaceous  and  allied  soils,  owring  to  their  retentive 
nature,  are  very  unstable  under  the  action  of  water  and  frost,  and 
in  their  natural  condition  afford  a  poor  foundation.  The  prepara- 


335 


70  HIGHWAY  CONSTRUCTION 

tion  of  such  soil  is  effected  by  drainage  and  by  the  application  of  a 
layer  of  suitable  material  to  entirely  separate  the  surface  from  the 
road  material.  This  material  may  be  sand,  furnace  ashes,  or  other 
material  of  a  similar  nature,  spread  in  a  layer  from  3  to  6  inches 
thick  over  the  surface  of  the  natural  soil. 

When  the  road  is  formed  in  rock  cuttings  it  is  advisable  to 
spread  a  layer  of  sand  or  other  material  of  light  nature,  so  as  to 
fill  up  the  irregularities  of  the  surface  as  well  as  to  form  a  cushion 
for  the  road  material  to  rest  on. 

Spreading  the  Stone.  The  stone  should  be  hauled  upon  the 
roadbed  in  broad-tire  two-wheeled  carts  and  dumped  in  heaps  and 
be  spread  evenly  with  a  rake  in  a  layer  which  should  be  of  a  depth 
of  4}  inches. 

Watering.  Wetting  the  stone  expedites  the  consolidation, 
decreases  crushing  under  the  roller,  and  assists  the  filling  of  the 
voids  with  the  binder.  It  should  be  applied  by  a  sprinkler  and 
should  not  be  thrown  on  in  quantity  or  from  the  plain  nozzle  of  a 
hose. 

Excessive  watering,  especially  in  the  earlier  stages,  tends  to 
soften  the  foundation,  and  care  should  be  exercised  in  its  appli- 
cation. 

Binding.  As  the  voids  in  loosely  spread  broken  stone  range 
from  35  to  50  per  cent  of  the  volume,  and  as  no  amount  of  rolling 
will  reduce  the  voids  more  than  one-half,  it  is  necessary,  in  order  to 
form  an  impervious  and  compact  mass,  to  add  some  fine  material 
which  is  called  the  binder.  It  may  consist  of  the  fragments  and 
detritus  obtained  in  crushing  the  stone.  When  this  is  insufficient, 
as  will  be. the  case  with  the  harder  rocks,  the  deficiency  may  be 
made  up  of  clean  sand  or  gravel.  The  proportion  of  binder 
should  slightly  exceed  the  voids  in  the  aggregate;  it  must  not  be 
mixed  with  the  stones,  but  should  be  spread  uniformly  in  small 
quantities  over  the  surface  and  rolled  into  the  interstices  with  the 
aid  of  water  and  brooms. 

As  the  quality  of  the  binding  used  is  of  vital  importance,  the 
employment  of  inferior  material,  such  as  road  scrapings  or  material 
of  a  clayey  nature,  should  be  avoided,  even  if  tke  initial  cost  of  the 
work  should  be  greater  when  a  good  binding  material  is  used. 


HIGHWAY  CONSTRUCTION  71 

Stone  consolidated  with  improper  binding  material  may  present 
a  good  appearance  immediately  after  being  rolled  and  be  otherwise 
an  apparently  good  piece  of  work,  still  in  damp  weather  a  consider- 
able amount  of  "lick-Ing  up"  by  the  wheels  of  the  vehicles  will  take 
place,  which  reduces  the  strength  of  the  coating  and  causes  the  sur- 
face to  wear  unequally. 

By  the  application  of  an  immoderate  quantity  of  binding  of  any 
description  the  stone  coating  will  become  unsound  or  rotten  in  con- 
dition, and  if  the  binding  be  of  an  argillaceous  nature,  it  will  expand 
during  frost,  owing  to  its  absorbent  properties,  and  cause  the  dis- 
placement of  the  stones.  The  surface  will  become  sticky,  which 
seriously  affects  the  tractive  power  of  horses,  while  the  road  itself 
will  suffer  by  the  irregular  deterioration  of  the  surface. 

The  use  of  such  material  as  mentioned  for  binding  enables 
rolling  to  be  accomplished  in  much  less  time  than  when  proper  bind- 
ing is  used,  and  the  cost  of  consolidating  the  stone  may  be  reduced 
by  25  per  cent;  but,  on  the  other  hand,  the  stone  coating  which  will 
probably  contain  under  these  circumstances  from  30  to  40  per  cent 
of  soft  and  soluble  matter,  and  possibly  present  a  smooth  surface 
immediately  after  being  rolled,  will  quickly  become  "cupped"  by 
the  wheel  traffic,  a  bumpy  surface  being  the  result.  This  is  caused 
by  the  irregular  wear,  while  the  lasting  qualities  or  "life"  of  the 
coating  will  be  shortened,  giving  unsatisfactory  results  to  those 
traveling  over  the  road,  and  the  work  of  renewing  the  surface  of 
the  road  in  this  manner  may  prove  a  failure  on  economical  grounds. 
There  can  be  no  doubt,  and  it  is  now  being  more  generally  recog- 
nized, that  sand  as  a  material  for  binding  in  connection  with  rolling 
operations,  when  applied  in  a  limited  but  sufficient  quantity,  pro- 
motes the  durability-  of  the  stone  coating,  while  the  general  results 
are  equally  satisfactory;  a  firm,  compact,  and  smooth  surface  is 
obtained,  and  the  subsequent  maintenance  of  the  road  is  minimized. 

A  great  amount  of  rolling  is  necessa/y  when  sand  is  employed 
as  a  binding  material,  but  economy  is  promoted,  and  the  results  are 
more  satisfactory  when  sand  is  used  than  by  the  use  of  the  material 
which  gives  to  the  stone  an  appearance  only  of  having  been  properly 
consolidated.  If  clean  sand  be  used  in  combination  with  the  screen- 
ings from  the  crusher  a  very  satisfactory  surface  will  be  obtained. 


72  .        HIGHWAY  CONSTRUCTION 

If  the  use  of  motor  vehicles  equipped  with  pueumatic  tires  be- 
comes general,  it  is  possible  that  some  other  description  of  binding 
material  will  be  necessary.  The  pumping  action  of  suction  created 
by  pneumatic  tires,  especially  when  propelled  at  a  high  speed,  causes 
a  considerable  movement  of  the  fine  particles  of  the  binding  material, 
which  on  being  displaced  will  convert  the  covering  into  a  mass  of 
stones.  This  objection  can  probably  be  overcome  by  watering. 

Compacting  the  Broken  Stone.  Three  methods  of  compacting 
the  broken  stone  are  practiced :  (1 )  by  the  traffic  passing  over  the  road ; 
(2)  by  rollers  drawn  by  horses ;  (3)  by  rollers  propelled  by  steam. 

The  first  method  is  both  defective  and  objectionable.  (1)  It  is 
destructive  to  the  horses  and  vehicles  using  the  road.  (2)  It  is  waste- 
ful of  material ;  about  one-third  of  the  stone  is  worn  away  in  the  oper- 
ation. (3)  Dung  and  dust  are  ground  up  with  the  stone,  and  the 
road  is  more  readily  affected  by  wet  and  frost. 

Steam=rollers  were  first  successfully  introduced  in  France  in  1860, 
since  which  time  they  have  been  almost  universally  adopted  on  account 
of  the  superiority  and  economy  of  the  work  done.  Their  use  shortens 
the  time  required  for  construction  or  repair,  and  effects  an  indirect 
saving  by  the  reduced  wear  and  tear  of  horses  and  vehicles.  They  are 
made  in  different  weights  ranging  from  3  to  30  tons.  For  the  compact- 
ing of  broken  stone  roads  the  weights  in  favor  are  from  ten  to  fifteen 
tons;  the  heavier  weights  are  considered  unwieldy  and  their  use  is 
liable  to  cause  damage  to  the  underground  structures  that  may  be  in 
the  roadway. 

The  advantage  of  steam  rolling  may  be  summed  up  as  follows: 

(1)  They  shorten  the  time  of  construction. 

(2)  A  saving  of  road  material,  (a)  because  there  are  no  loose 
stones  to  be  kicked  about  and  worn ;  (b)  because  there  is  no  abrasion 
of  the  stone,  only  one  surface  of  the  stone  being  exposed  to  wear;  (c) 
because  a  thinner  coating  of  stone  can  be  employed;  (d)  because  no 
ruts  can  be  formed  in  which  water  can  lie  to  rot  the  stone. 

(3)  Steam-rolled  roads  are  easier  to  travel  on  account  of  their 
even  surface  and  superior  hardness  and  they  have  a  better  appearance. 

(4)  The  roads  can  be  repaired  at  any  season  of  the  year. 

(5)  Saving  both  in  materials  and  manual  labor. 


338 


HIGHWAY  CONSTRUCTION 

PART  II 


STREETS  AND  HIGHWAYS 

CITY  STREETS 

The  first  work  requiring  the  skill  of  the  engineer  is  to  lay  out  town 
sites  properly,  especially  with  reference  to  the  future  requirements  of  a 
large  city  where  any  such  possibility  exists.  Few  if  any  of  our  large 
cities  were  so  planned.  The  same  principles,  to  a  limited  extent,  are 
applicable  to  all  towns  or  cities.  The  topography  of  the  site  should  be 
carefully  studied,  and  the  street  lines  adapted  to  it.  These  lines 
should  be  laid  out  systematically,  with  a  view  to  convenience  and 
comfort,  and  also  with  reference  to  economy  of  construction,  future 
sanitary  improvements,  grades,  and  drainage. 

Arrangement  of  City  Streets.  Generally,  the  best  method  of 
laying  out  streets  is  in  straight  lines,  with  frequent  and  regular  inter- 
secting streets,  especially  for  the  business  parts  of  a  city.  When  there 
is  some  centrally  located  structure,  such  as  a  courthouse,  city  hall, 
market,  or  other  prominent  building,  it  is  very  desirable  to  have  several 
diagonal  streets  leading  thereto.  In  the  residence  portions  of  cities, 
especially  if  on  hilly  ground,  curves  may  with  advantage  replace 
straight  lines,  by  affording  better  grades  at  less  cost  of  grading,  and  by 
improving  property  through  avoiding  heavy  embankments  or  cuttings. 

Width  of  Streets.  The  width  of  streets  should  be  proportioned 
to  the  character  of  the  traffic  that  will  use  them.  No  rule  can  be  laid 
down  by  which  to  determine  the  best  width  of  streets ;  but  it  may  safely 
be  said  that  a  street  which  is  likely  to  become  a  commercial  thorough- 
fare should  have  a  width  of  not  less  than  120  feet  between  the  building 
lines — the  carriage-way  80  feet  wide,  and  the  sidewalks  each  20  feet 
wide. 

In  streets  occupied  entirely  by  residences  a  carriage-way  32  feet 
wide  will  be  ample,  but  the  width  between  the  building  lines  may  be  as 
great  as  desired.  The  sidewalks  may  be  any  amount  over  10  feet 

Copyright,  1908,  by  American  School  of  Corespondence. 


341 


74 


HIGHWAY  CONSTRUCTION 


which  fancy  dictates.  Whatever  width  is  adopted  for  them,  not  more 
of  it  than  8  feet  need  be  paved,  the  remainder  being  occupied  with 
grass  and  trees. 

Street  Grades.  The  grades  of  city  streets  depend  upon  the 
topography  of  the  site. .  The  necessity  of  avoiding  deep  cuttings  or 
high  embankments  which  would  seriously  affect  the  value  of  adjoining 
property  for  building  purposes,  often  demands  steeper  grades  than 
are  permissible  on  country  roads.  Many  cities  have  paved  streets 
on  20  per  cent  grades.  In  establishing  grades  through  unimproved 
property,  they  may  usually  be  laid  with  reference  to  securing  the  most 
desirable  percentage  within  a  proper  limit  of  cost.  But  when  improve- 
ments have  already  been  made  and  have  been  located  with  reference 
to  the  natural  surface  of  the  ground,  giving  a  desirable  grade  is  fre- 
quently a  matter  of  extreme  difficulty  without  injury  to  adjoining 
property.  In  such  cases  it  becomes  a  question  of  how  far  individual 

interests  shall  be  sacrificed  to  the 
general  good.  There  are,  how- 
ever, certain  conditions  which  it  is 
important  to  bear  in  mind: 

(1)  That   the    longitudinal 
crown  level  should  be  uniformly 
sustained    from    street"  to   street 
intersection,  whenever  practicable. 

(2)  That  the  grade  should 
be  sufficient  to  drain  the  surface. 

(3)  That  the  crown  levels  at 
all    intersections    should  be    ex- 
tended transversely,  to  avoid  form- 
ing a  depression  at  the  junction. 

Arrangements  of  Grades  at  Street  Intersections.  The  best  ar- 
rangement for  intersections  of  streets  when  either  or  both  have  much 
inclination,  is  a  matter  requiring  much  consideration,  and  is  one  upon 
which  much  diversity  of  opinion  exists.  No  hard  or  fast  rule  can  be 
laid  down;  each  will  require  special  adjustment.  The  best  and  sim- 
plest method  is  to  make  the  rectangular  space  aaaaaaaa,  Fig.  47, 
level,  with  a  rise  of  one-half  inch  in  10  feet  from  AAAA  to  B,  placing 
gulleys  at  AAAA  and  the  catch  basins  at  ccc.  When  this  method  is 
not  practicable,  adopt  such  a  grade  (but  one  not  exceeding  2£  per  cent) 


342 


HIGHWAY  CONSTRUCTION 


75 


that  the  rectangle  AAAA  shall  appear  to  be  nearly  level;  but  to  secure 
this  it  must  actually  have  a  considerable  dip  in  the  direction  of  the 
slope  of  the  street.  If  steep  grades  are  continued 'across  intersections, 
they  introduce  side  slopes  in  the  streets  thus  crossed,  which  are  trouble- 
some, if  not  dangerous,  to  vehicles  turning  the  corners,  especially  the 
upper  ones.  Such  intersections  are  especially  objectionable  in  rainy 


300 


300 


30Q 


Fig.  48. 

weather.  The  storm  water  will  fall  to  the  lowest  point,  concentrating 
a  large  quantity  of  water  at  two  receiving  basins,  which,  with  a  broken 
grade,  could  be  divided  betwreen  four  or  more  basins. 

Fig.  48  shows  the  arrangement  of  intersections  in  steep  grades 
adapted  for  the  streets  of  Duluth,  Minn.  From  this  it  will  be  seen 
that  at  these  intersections  the  grades  are  flattened  to  three  per  cent  for 
the  width  of  the  roadway  of  the  intersecting  streets,  and  that  the  grade 
of  the  curbs  is  flattened  to  eight  per  cent  for  the  width  of  the  intersecting 
sidewalks.  Grades  of  less  amount  on.  roadway  or  sidewalk  are  con- 
tinuous. The  elevation  of  block-corners  is  found  by  adding  together 
the  curb  elevations  at  the  faces  of  the  block-corners,  and  2J  per  cent  of 


343 


76  HIGHWAY  CONSTRUCTION 


the  sum  of  the  widths  of  the  two  sidewalks  at  the  corner,  and  dividing 
the  whole  by  two.  This  gives  an  elevation  equal  to  the  average  eleva- 
tion of  the  curbs  at  the  corners,  plus  an  average  rise  of  two  and  one- 
half  per  cent  across  the  width  of  the  sidewalk. 

Accommodation  summits  have  to  be  introduced  between  street 
intersections — first,  in  hilly  localities,  to  avoid  excessive  excavation; 
and  second,  when  the  intersecting  streets  are  level  or  nearly  so,  for  the 
purpose  of  obtaining  the  fall  necessary  for  surface  drainage. 

The  elevation  and  location  of  these  summits  may  be  calculated 
as  follows :  Let  A  be  the  elevation  of  the  highest  corner;  B,  the  eleva- 
tion of  the  lowest  corner;  D,  the  distance  from  corner  to  corne:*; 
and  R,  the  rate  of  the  accommodation  grade.  The  elevation  of  the 
summit  is  equal  to 

D-R  +  A  +  B. 
2 

The  distance  from  A  or  B  is  found  by  subtracting  the  elevation  of 
either  A  or  B  from  this  quotient,  and  dividing  the  result  by  the  rate 
of  grade.  Or  the  summits  may  be  located  mechanically  by  specially 
prepared  scales.  Prepare  two  scales  divided  to  correspond  to  the  rate 
of  grade;  that  is,  if  the  rate  of  grade  be  1  foot  per  100  feet,  then  one 
division  of  the  scale  should  equal  100  feet  on  the  map  scale.  These 
divisions  may  be  subdivided  into  tenths.  One  scale  should  read  from 
right  to  left,  and  one  from  left  to  right. 

To  use  the  scales,  place  them  on  the  map  so  that  their  figures 
correspond  with  the  corner  elevations;  then,  as  the  scales  read  in  op- 


—  «•  •*  """  £ortom    of  Suffer  *""*  "•—  —* 

Fig.  49. 

posite  directions,  there  is  of  course  some  point  at  which  the  opposite 
readings  will  be  the  same:  this  point  is  the  location  of  the  summits; 
and  the  figures  read  off  the  scale  its  elevation.  If  the  difference  in 
elevation  of  the  corners  is  such  as  not  to  require  an  intermediate  sum- 
mit for  drainage,  it  will  be  apparent  as  soon  as  the  scales  are  placed 
in  position. 

When  an  accommodation  summit  is  employed,  it  should  be  form- 
ed by  joining  the  two  straight  grade  lines  by  a  vertical  curve,  as 


344 


HIGHWAY  CONSTRUCTION 


77 


described  in  Part  I.  The  curve  should  be  used  both  in  the  crown  of 
the  street  and  in  the  curb  and  footpath. 

Where  the  grade  is  level  between  intersections,  sufficient  fall  for 
surface  drainage  may  be  secured  without  the  aid  of  accommodation 
summits,  by  arranging  the  grades  as  shown  in  Fig.  49.  The  curb  is 
set  level  between  the  corners;  a  summit  is  formed  in  the  gutter;  and 
receiving  basins  are  placed  at  each  corner. 

Transverse  Grade.  In  transverse  grade  the  street  should  be 
level;  that  is,  the  curbs  on  opposite  sides  should  be  at  the  same  level, 
and  the  street  crown  rise  equally  from  each  side  to  the  center.  But  in 
hillside  streets  this  condition  cannot  always  be  fulfilled,  and  opposite 


Fig.  52. 


sides  of  the  street  may  differ  as  much  as  five  feet;  in  such  cases  the 
engineer  will  have  to  use  his  discretion  as  to  whether  he  shall  adopt  a 
straight  slope  inclining  to  the  lower  side,  thus  draining  the  whole  street 
by  the  lower  gutter,  or  adopt  the  three-curb  method  and  sod  the  slope 
of  the  higher  side. 

In  the  improvement  of  old  streets  with  the  sides  at  different  levels, 
much  difficulty  will  be  met,  especially  where  shade  trees  have  to  be 
spared.  In  such  cases,  recognized  methods  have  to  be  abandoned,  and 
the  engineer  will  have  to  adopt  methods  of  overcoming  the  difficulties 
in  accordance  with  the  conditions  and  necessities  of  each  particular 
case.  Figs.  50,  51,  and  52  illustrate  several  typical  arrangements  in 


345 


78  HIGHWAY  CONSTRUCTION 


the  case  of  streets  in  which  the  opposite  sides  are  at  different  levels. 
Transverse  Contour  or  Crown.  The  reason  for  crowning  a  pave- 
ment— i.  e.,  making  the  center  higher  than  the  sides — is  to  provide 
for  the  rapid  drainage  of  the  surface.  The  most  suitable  form  for  the 
crown  is  the  parabolic  curve,  which  may  be  started  at  the  curb  line, 
or  at  the  edge  of  the  gutter  adjoining  the  carriage-way  about  one  foot 


Fig.  53. 


from  the  curb.  Fig.  53  shows  this  form,  which  is  obtained  by  dividing 
the  ordinate  or  width  from  the  gutter  to  tne  center  of  the  street  into  ten 
equal  parts,  and  raising  perpendiculars  the  length  of  which  will  be 
determined  by  multiplying  the  rise  at  the  center  by  the  respective 
number  of  each  perpendicular  in  the  diagram.  The  amounts  thus 
obtained  can  be  added  to  the  rod  readings;  and  the  stakes,  set  at  the 
proper  distance  across  the  street,  with  their  tops  at  this  level,  will  give 
the  required  curve. 

The  amount  of  transverse  rise,  or  the  height  of  the  center  above 
the  gutters,  varies  with  the  different  paving  materials,  smooth  pave- 
ments requiring  the  least,  and  rough  ones  and  earth  the  greatest.  The 
rise  is  generally  stated  in  a  proportion  of  the  width  of  the  carriage-way. 
The  most  suitable  proportions  are: 

Stone  blocks,  rise  at  center,  Js  width  of  carriage-way. 
Wood     '  TJ-n     ' 

Brick  ;sV 

Asphalt"         "      "       "          «V      " 

Sub-Foundation  Drainage  of  Streets.  The  sub-foundation 
drainage  of  streets  cannot  be  effected  by  transverse  drains,  because  of 
their  liability  to  disturbance  by  the  introduction  of  gas,  water,  and 
other  pipes. 

Longitudinal  drains  must  be  depended  upon  entirely;  they  may 
be  constructed  of  the  same  materials  and  in  the  same  manner  as  road 
drains.  The  number  of  these  longitudinal  drains  must  depend  upon 


346 


HIGHWAY  CONSTRUCTION  79 


the  character  of  the  soil.  If  the  soil  is  moderately  retentive,  a  single 
row  of  tiles  or  a  .hollow  invert  placed  under  the  sewer  in  the  center  of 
the  street  will  generally  be  sufficient;  or  two  rows  of  tiles  may  be  em- 
ployed, one  placed  outside  each  curb  line;  if,  on  the  other  hand,  the 
soil  is  exceedingly  wet  and  the  street  very  wide,  four  or  more  lines 
may  be  employed.  These  drains  may  be  permitted  to  discharge  into 
the  sewers  of  the  transverse  streets. 

Surface  Drainage.  The  removal  of  water  falling  on  the  street 
surface  is  provitled  for  by  collecting  it  in  the  gutters,  from  which  it  is 
discharged  into  the  sewers  or  other  channels  by  means  of  catch-basins 
placed  at  all  street  intersections  and  dips  in  the  street  grades. 

Gutters.  The  gutters  must  be  of  sufficient  depth  to  retain  all  the 
water  which  reaches  them  and  prevent  its  overflowing  on  the  footpath. 
The  depth  should  never  be  less  than  6  inches,  and  very  rarely  need  be 
more  than  10  inches. 

Catch=basins  are  of  various  forms,  usually  circular  or  rectangular, 
built  of  brick  masonry  coated  with  a  plaster  of  Portland  cement. 
Whichever  form  is  adopted,  they  should  fulfil  the  following  conditions: 

(1)  The  inlet  and  outlet  should  have  sufficient  capacity  to  receive 
and  discharge  all  water  reaching  the  basin. 

(2)  The  basins  should  have  sufficient  capacity  below  the  outlet 
to  retain  all  sand  and  road  detritus,  and  prevent  it  being  carried  into 
the  sewer. 

(3)  They  should  be  trapped  so  as  to  prevent  the  escape  of  sewer 
gas.     (This  requirement  is   frequently  omitted,  to  the  detriment  of 
the  health  of  the  people.) 

(4)  They  should  be  constructed  so  that  the  pit  can  easily  be 
cleaned  out. 

(5)  The  inlet  should  be  so  constructed  as  not  easily  to  be  choked 
by  leaves  or  debris. 

(6)  They  must  offer  the  least  possible  obstruction  to  traffic. 

(7)  The  pipe  connecting  the  basin  to  the  sewer  should  be  easily 
freed  of  any  obstruction. 

-  The  bottom  of  the  basins  should  be  6  or  8  feet  below  the  street 
level ;  and  the  water  level  in  them  should  be  from  3  to  4  feet  lower  than 
the  street  surface,  as  a  protection  against  freezing. 

The  capacity  and  number  of  basins  will  depend  upon  the  area  of 
surface  which  they  drain 


347 


80  HIGHWAY  CONSTRUCTION 


In  streets  having  level  or  light  longitudinal  grades,  gullies  may  be 
formed  along  the  line  of  the  gutter  at  such  intervals  as  may  be  found 
necessary. 

Catch-basins  are  usually  placed  at  the  curb  line.  In  several  cities, 
the  basin  is  placed  in  the  center  of  the  street,  and  connects  to 
inlets  placed  at  the  curb  line.  This  reduces  the  cost  of  construction 
and  cleaning,  and  removes  from  the  sidewalk  the  dirty  operations  of 
cleaning  the  basins. 

Catch-basins  and  gully-pits  require  to  be  cleaned  out  at  frequent 
intervals;  otherwise  the  odor  arising  from  the  decomposing  matter 
contained  in  them  will  be  very  offensive.  No  rule  can  be  laid  down 
for  the  intervals  at  which  the  cleaning  should  be  done,  but  they  must 
be  cleaned  often  enough  to  prevent  the  matter  in  them  from  putrefying. 
There  is  no  uniformity  of  practice  observed  by  cities  in  this  matter;  in 
some,  the  cleaning  is  done  but  once  a  year;  in  others,  after  every  rain- 
storm; in  still  others,  at  intervals  of  three  or  four  months;  while  in  a 
few  cities  the  basins  are  cleaned  out  once  a  month. 

FOUNDATIONS 

•  The  stability,  permanence,  and  maintenance  of  any  pavement 
depend  upon  its  foundation.  If  the  foundation  is  weak,  the  surface 
will  soon  settle  unequally,  forming  depressions  and  ruts.  With  a  good 
foundation,  the  condition  of  the  surface  will  depend  upon  the  material 
employed  for  the  pavement  and  upon  the  manner  of  laying  it. 

The  essentials  necessary  to  the  forming  of  a  good  foundation  are : 

(1)  The  entire  removal  of  all  vegetable,  perishable,  and  yielding 
matter.     It  is  of  no  use  to  lay  good  material  on  a  bad  substratum. 

(2)  The  drainage  of  the  subsoil  wherever  necessary.     A  per- 
manent foundation  can  be  secured  only  by  keeping  the  subsoil  dry; 
for,  where  water  is  allowed  to  pass  into  and  through  it,  its  weak  spots 
will  be  quickly  discovered  and  settlement  will  take  place. 

(3)  The  thorough  compacting  of  the  natural  soil  by  .rolling  with 
a  roller  of  proper  weight  and  shape  until  it  forms  a  uniform  and  un- 
yielding surface. 

(4)  The  placing  on  the  natural  soil  so  compacted,  a  sufficient 
thickness  of  an  impervious  and  incompressible  material  to  cut  off  all 
communication  between  the  soil  and  the  bottom  of  the  pavement. 

The  character  of  the  natural  soil  over  which  the  roadway  is  to  be 
built  has  an  important  bearing  upon  the  kind  of  foundation  and  the 
manner  of  forming  it;  each  class  of  soil  will  require  its  own  special 


348 


HIGHWAY  CONSTRUCTION  81 


treatment.  Whatever  its  character,  it  must  be  brought  to  a  dry  and 
tolerably  hard  -condition  by  draining  and  rolling.  Sand  and  gravels 
which  do  not  hold  water,  present  no  difficulty  in  securing  a  solid  and 
secure  foundation;  clays  and  soils  retentive  of  water  are  the  most 
difficult.  Clay  should  be  excavated  to  a  depth  of  at  least  18  inches 
below  the  surface  of  the  finished  covering;  and  the  space  so  excavated 
should  be  filled  in  with  sand,  furnace  slag,  ashes,  coal  dust,  oyster 
shells,  broken  brick,  or  other  materials  which  are  not  excessively  absorb- 
ent of  water.  A  clay  soil  or  one  retaining  water  may  be  cheaply  and 
effectually  improved  by  laying  cross-drains  wTith  open  joints  at  inter- 
vals of  50  or  100  feet.  These  drains  should  be  not  less  than  18  inches 
below  the  surface,  and  the  trenches  filled  with  gravel.  They  should 
be  4  inches  in  internal  diameter,  and  should  empty  into  longitudinal 
drains. 

Sand  and  planks,  gravel,  and  broken  stone  have  been  successively 
used  to  form  the  foundation  for  pavements;  but,  although  eminently 
useful  materials,  their  application  to  this  purpose  has  always  been  a 
failure.  Being  inherently  weak  and  possessing  no  cohesion,  the  main 
reliance  for  both  strength  and  wear  must  be  placed  upon  the  surface- 
covering.  This  covering — usually  (except  in  case  of  sheet  asphalt) 
composed  of  small  units,  with  joints  between  them  varying  from  one- 
half  an  inch  to  one  and  a-half  inches — possesses  no  elements  of  cohe- 
sion; and  under  the  blows  and  vibrations  of  traffic  the  independent 
units  or  blocks  will  settle  and  be  jarred  loose.  On  account  of  their 
porous  nature,  the  subsoil  quickly  becomes  saturated  with  urine  and 
surface  waters,  which  percolate  through  the  joints;  winter  frosts  up- 
heave them ;  and  the  surface  of  the  street  becomes  blistered  and  broken 
up  in  dozens  of  places. 

Concrete.  As  a  foundation  for  all  classes  of  pavement  (broken 
stone  excepted),  hydraulic-cement  concrete  is  superior  to  any  other. 
\Yhen  properly  constituted  and  laid,  it  becomes  a  solid,  coherent  mass 
capable  of  bearing  great  weight  without  crushing.  If  it  fail  at  all,  it 
must  fail  altogether.  The  concrete  foundation  is  the  most  costly,  but  this 
is  balanced  by  its  permanence  and  by  the  saving  in  the  cost  of  repairs  to 
the  pavement  which  it  supports.  It  admits  of  access  to  subterranean 
pipes  with  less  injury  to  the  neighboring  pavement  than  any  other,  for 
the  concrete  may  be  broken  through  at  any  point  without  unsettling 
the  foundation  for  a  considerable  distance  around  it,  as  is  the  case  with 


349 


82  HIGHWAY  CONSTRUCTION 


sand  or  other  incoherent  material;  and  when  the  concrete  is  replaced 
and  set,  the  covering  may  be  reset  at  its  proper  level,  without  the  un- 
certain allowance  for  settlement  which  is  necessary  in  other  cases. 

Thickness  of  Concrete.  The  thickness  of  the  concrete  bed  must 
be  proportioned  by  the  engineer;  it  should  be  sufficient  to  provide 
against  breaking  under  transverse  strain  caused  by  the  settlement  of 
the  subsoil.  On  a  well-drained  soil,  six  inches  will  be  found  sufficient; 
but  in  moist  and  clayey  soils,  twelve  inches  will  not  be  excessive.  On 
such  soils  a  layer  of  sand  or  gravel,  spread  and  compacted  before  pla- 
cing the  concrete,  will  be  found  very  beneficial. 

The  proportions  of  the  ingredients  for  concrete  used  for  pavement 
foundations  are  usually: 

1  part  Portland  cement 
3  parts  Sand 
7  parts  Broken  Stone. 
Or, 

1  part  Natural  Hydraulic  Cement 

2  parts  Sand 

5  parts  Broken  Stone. 

The  question  is  sometimes  raised  as  to  whether  Natural  or  Port- 
land cement  should  be  used.  Natural  cement  is  more  extensively 
employed  on  account  of  its  being  cheaper  in  price  than  Portland. 
There  is  no  advantage  gained  in  using  Portland  cement.  Concrete 
should  not  be  laid  when  the  temperature  falls  below  32°  F. 

The  concrete  foundation,  after  completion,  should  be-  allowed  to 
remain  several  days  before  the  pavement  is  placed  upon  it,  in  order 
that  the  mortar  may  become  entirely  set.  During  setting,  the  con- 
crete should  be  protected  from  the  drying  action  of  the  sun  and 
wind,  and  should  be  kept  damp  to  prevent  the  formation  of  drying 
cracks. 

STONE  BLOCK  PAVEMENTS 

Stone  blocks  are  commonly  employed  for  pavements  where  traffic 
is  heavy.  The  material  of  which  the  blocks  are  made  should  possess 
sufficient  hardness  to  resist  the  abrasive  action  of  traffic,  and  sufficient 
toughness  to  prevent  them  from  being  broken  by  the  impact  of  loaded 
wheels.  The  hardest  stones  will  not  necessarily  give  the  best  re- 
suits  in  the  pavement,  since  a  very  hard  stone  usually  wears  smooth 
and  becomes  slippery.  The  edges  of  the  block  chip  off,  and  the 


350 


HIGHWAY  CONSTRUCTION  83 

upper   face    becomes    rounded,   thus   making   the    pavement    very 
rough. 

The  stone  is  sometimes  tested  to  determine  its  strength,  resistance 
to  abrasion,  etc. ;  but,  as  the  conditions  of  use  are  quite  different  from 
those  under  which  it  may  be  tested,  such  tests  are  seldom  satisfactory. 
However,  examination  of  a  stone  as  to  its  structure,  the  closeness  of  its 
grain,  its  homogeneity,  porosity,  etc.,  may  assist  in  forming  an  idea  of 
its  value  for  use  in  a  pavement.  A  low  degree  of  permeability  usually 
indicates  that  the  material  will  not  be  greatly  affected  by  frost. 

Materials. — Granite.  Granite  is  more  extensively  employed  for 
stone  block  paving  than  any  other  variety  of  stone;  and  because  of  this 
fact,  the  term  "granite  paving"  is  generally  used  as  being  synonymous 
with  stone  block  paving.  The  granite  employed  should  be  of  a  tough, 
homogeneous  nature.  The  hard,  quartz  granites  are  usually  brittle, 
and  do  not  wear  well  under  the  blows  of  horses'  feet  or  the  impact  of 
vehicles;  granite  containing  a  high  percentage  of  feldspar  will  be  inju- 
riously affected  by  atmospheric  changes;  and  granite  in  which  mica 
predominates  will  wear  rapidly  on  account  of  its  laminated  structure. 
Granite  possesses  the  very  important  property  of  splitting  in  three 
planes  at  right  angles  to  one  another,  so  that  paving  blocks  may  readily 
be  formed  with  nearly  plane  faces  and  square  corners.  This  property 
is  called  the  rift  or  cleavage. 

Sandstones  of  a  close-grained,  compact  nature  often  give  very 
satisfactory  results  under  heavy  traffic.  They  are  less  hard  than 
granite,  and  wear  more  rapidly,  but  do  not  become  smooth  and  slip- 
pery. Sandstones  are  generally  known  in  the  market  by  the  name 
of  the  quarry  or  place  where  produced  as  "Medina,"  "Berea," 
etc. 

Trap  rock,  while  answering  well  the  requirements  as  to  durability 
and  resistance  to  wear,  is  objectionable  on  account  of  its  tendency  to 
wear  smooth  and  become  slippery;  it  is  also  difficult  to  break  into 
regular  shapes. 

Limestone  has  not  usually  been  successful  in  use  for  the  construc- 
tion of  block  pavements,  on  account  of  its  lack  of  durability  against 
atmospheric  influences.  The  action  of  frost  commonly  splits  the 
blocks;  and  traffic  shivers  them,  owing  to  the  lamination  being 
vertical. 


851 


HIGHWAY  CONSTRUCTION 


TABLE  12. 

Specific  Gravity,  Weight,  Resistance  to  Crushing,  and 
Absorption  Power  of  Stones. 


MATERIAL 

SPECIFIC 
GRAVITY 

WEIGHT 

Pounds 
per  cu.  ft. 

RESISTANCE 
TO  CRUSHING 
Pounds 
per  sq.  in. 

PERCENTAGE 
OF  WATER 
ABSORBED 

Granite  — 
Maximum  

2.80 

176 

35,000 

0.155 

Minimum  
Trap  — 
Maximum  
Minimum  
Sandstone  — 

2.60 

3.03 

2.86 

2.75 

163 

178 
189 

170 

12,000 

24.000 
19.000 

18.000 

0.066 

0.019 
0.000 

5.4PO 

Minimum  
Limestone  — 

2.23 

2.75 

137 
175 

5,000 
20.000 

0.410 
5.000 

1.90 

118 

7,01)0 

0.200 

Brick  Paving  — 

1.95 

20.000 

Minimum 

2.55 

10,000 

Cobblestone  Pavement.  Cobblestones  bedded  in  sand  possess 
the  merit  of  cheapness,  and  afford  an  excellent  foothold  for  horses; 
but  the  roughness  of  such  pavements  requires  the  expenditure  of  a 
large  amount  of  tractive  energy  to  move  a  load  over  them.  Aside  from 
this,  cobblestones  are  entirely  wanting  in  the  essential  requisites  of  a 
good  pavement.  The  stones  being  of  irregular  size,  it  is  almost  impos- 
sible to  form  a  bond  or  to  hold  them  in  place.  Under  the  action  of  the 
traffic  and  frost,  the  roadway  soon  becomes  a  mass  of  loose  stones. 
Moreover,  cobblestone  pavements  are  difficult  to  keep  clean,  and  very 
unpleasant  to  travel  over. 

Belgian  Block  Pavement.  Cobblestones  were  displaced  by  pave- 
ments formed  of  small  cubical  blocks  of  stone.  This  type  of 
pavement  was  first  laid  in  Brussels,  thence  imported  to  Paris,  and  from 
there  taken  to  the  United  States,  where  it  has  been  widely  known  as 
the  "Belgian  block"  pavement.  It  has  been  largely  used  in  New  York 
City,  Brooklyn,  and  neighboring  towns,  the  material  being  trap-rock 
obtained  from  the  Palisades  on  the  Hudson  River. 

The  stones,  being  of  regular  shape,  remain  in  place  better  than 
cobblestones;  but  the  cubical  form  (usually  five  inches  in  each  dimen- 
sion) is  a  mistake.  The  foothold  is  bad;  the  stones  wear  round;  and 
the  number  of  joints  is  so  great  that  ruts  and  hollows  are  quickly 
formed.  This  pavement  offers  less  resistance  to  traction  than  cobble- 
stones, but  it  is  almost  equally  rough  and  noisy. 

Granite  Block  Pavement.    The  Belgian  block  has  been  gradually 


359 


HIGHWAY  CONSTRUCTION  85 

displaced  by  the  introduction  of  rectangular  blocks  of  granite.  Blocks 
of  comparatively  large  dimensions  were  at  first  employed.  They  were 
from  6  to  8  inches  in  width  on  the  surface,  from  10  to  20  inches  in 
length,  with  a  depth  of  9  inches.  They  were  merely  placed  in  rows 
on  the  subsoil,  perfunctorily  rammed,  the  joints  filled  with  sand,  and 
the  street  thrown  open  to  traffic.  The  unequal  settlement  of  the 
blocks,  the  insufficiency  of  the  foothold,  and  the  difficulty  of  cleansing 
the  street,  led  to  the  gradual  development  of  the  latest  type  of  stone- 
block  pavement,  wrhich  consists  of  narrow,  rectangular  .blocks  of 
granite,  properly  proportioned,  laid  on  an  unyielding  and  impervious 
foundation,  with  the  joints  between  the  blocks  filled  with  an  imper- 
meable cement. 

Experience  has  proved  beyond  doubt  that  this  latter  type  of 
pavement  is  the  most  enduring  ai  d  economical  for  roadways  subjected 
to  heavy  and  constant  traffic.  Its  advantages  are  many,  while  its 
defects  are  few. 

Advantages. 

(1)  Adaptability    to    all    grades. 

(2)  Suits  all  classes  of  traffic. 

(3)  Exceedingly   durable. 

(4)  Foothold,    fair. 

(5)  Requires  but  little  repair. 
(G)     Yields  but  little  dust  or  mud. 
(7)     Facility  for  cleansing,  fair. 
Defects. 

(1)  Under  certain  conditions  of  the  atmosphere,  the  surface  of 
the  pavement  becomes  greasy  and  slippery. 

(2)  The  incessant  din  and  clatter  occasioned  by  the  movement 
of  traffic  is  an  intolerable  nuisance;  it  is  claimed  by  many  physicians 
that  the  noise  injuriously  affects  the  nerves  and  health  of  persons  who 
are  obliged  to  live  or  do  business  in  the  vicinity  of  streets  so  paved. 

(3)  Horses  constantly  employed  upon  it  soon  suffer  from  the 
continual  jarring  produced  in  their  legs  and  hoofs,  and  quickly  wear 
out. 

(4)  The  discomfort  of  persons  riding  over  the  pavement  is  very 
great,  because  of  the  continual  jolting  to  which  they  are  subjected. 

(5)  If  stones  of  a,n  unsuitable  quality  are  used — for  example, 


383 


86  HIGHWAY  CONSTRUCTION 

those  that  polish — the  surface  quickly  becomes  slippery  and  exceed- 
ingly unsafe  for  travel. 

Size  and  Shape  of  Blocks.  The  proper  size  of  blocks  for  paving 
purposes  has  been  a  subject  of  much  discussion,  and  a  great  variety  of 
forms  and  dimensions  are  to  be  found  in  all  cities. 

For  stability,  a  certain  proportion  must  exist  between  the  depth, 
the  length,  and  the  breadth.  The  depth  must  be  such  that  when  the 
wheel  of  a  loaded  vehicle  passes  over  one  edge  of  the  upper  surface 
of  a  block,  the  block  will  not  tend  to  tip  up.  The  resultant  direction 
of  the  pressure  of  the  load  and  adjoining  blocks  should  always  tend 
to  depress  the  whole  block  vertically ;  where  this  does  not  happen,  the 
maintenance  of  a  uniform  surface  is  impossible.  To  fulfil  this  require- 
ment, it  is  not  necessary  to  make  the  block  more  than  six  inches  deep. 

Width  of  Blocks.  The  maximum  width  of  blocks  is  controlled 
by  the  size  of  horses'  hoofs.  To  afford  good  foothold  to  horses  draw- 
ing heavy  loads,  it  is  necessary  that  the  width  of  each  block,  measured 
along  the  street,  shall  be  the  least  possible  consistent  with  stability. 

Gutter  formed  of  3  rows  of 
blocks,  Set  /ongiruo/inal/y 


If  the  width  be  great,  a  horse  drawing  a  heavy  load,  attempting  to  find 
a  joint,  slips  back,  and  requires  an  exceptionally  wide  joint  to  pull  him 
up.  It  is  therefore  desirable  that  the  width  of  a  block  shall  not  exceed 
3  inches;  or  that  four  blocks,  taken  at  random  and  placed  side  by  side, 
shall  not  measure  more  than  14  inches. 

Length  of  Blocks,  The  length,  measured  across  the  street, 
must  be  sufficient  to  break  joints  properly,  for  two  or  more  joints  in 
line  lead  to  the  formation  of  grooves.  For  this  purpose  the  length 
of  the  block  should  be  not  less  than  9  inches  nor  more  than  12  inches. 

Form  of  Blocks.  The  blocks  should  be  well  squared,  and  must 
not  taper  in  any  direction;  sides  and  ends  should  be  free  from  irregular 
projections.  Blocks  that  taper  from  the  surface  downwards  (wedge- 
shaped)  should  not  be  permitted  in  the  work;  but  if  any  are  allowed, 
they  should  be  set  with  the  widest  side  down. 


854 


HIGHWAY  CONSTRUCTION 


S7 


Manner  of  Laying  Blocks-  The  blocks  should  be  laid  in  parallel 
courses,  with  their  longest  side  at  right  angles  to  the  axis  of  the  street, 
and  the  longitudinal  joints  broken  by  a  lap  of  at  least  two  inches  (see 
Figs.  54  and  55).  The  reason  for  this  is  to  prevent  the  formation  of 
longitudinal  ruts,  which  would  happen  if  the  blocks  were  laid  length- 
wise. Laying  blocks  obliquely  and  "herring-bone"  fashion  has  been 


j  1  (  T  |^~  -VA^_X  "-I 

;!           1           1           LI           1 
H        ~1           1           L         1 

..- 

1           i           1          1          1           I 

__ 

. 

1          1           (          L         1  ._, 

.  . 

(i       i       in       i 

1         1 

_      " 

!         1         1         1        1         1 

- 

r  i_      1       i       i      i- 

}|       i       i       i      i       i 

.. 

i       i       i       i      i 

Plan 
Fig.  55. 

tried  in  several  cities,  with  the  idea  that  the  wear  and  formation  of  ruts 
would  be  reduced  by  having  the  vehicle  cross  the  blocks  diagonally. 
The  method  has  failed  to  give  satisfactory  results;  the  wear  was  ir- 
regular and  the  foothold  defective;  the  difficulty  of  construction  was 
increased  by  reason  of  labor  required  to  form  the  triangular  joints;  and 
the  method  was  wasteful  of  material. 


Fig.  56. 


The  gutters  should  be  formed  by  three  or  more  courses  of  block, 
laid  with  their  length  parallel  to  the  curb- 

At  junctions  or  intersections  of  streets,  the  blocks  should  be  laid 
diagonally  from  the  center,  as  shown  in  Fig.  56.  The  reasons  for 


855 


HIGHWAY  CONSTRUCTION 


this  are:  (1)  To  prevent  the  traffic  crossing  the  intersection  from 
following  the  longitudinal  joints  and  thus  forming  depressions  and 
ruts;  (2)  Laid  in  this  manner,  the  blocks  afford  a  more  secure  foot- 
hold for  horses  turning  the  corners.  The  ends  of  the  diagonal  blocks 
where  they  abut  against  the  straight  blocks,  must  be  cut  to  the  re- 
quired bevel. 

The  blocks  forming  each  course  must  be  of  the  same  depth,  and 
no  deviation  greater  than  one-quarter  of  an  inch  should  be  permitted. 
The  blocks  should  be  assorted  as  they  are  delivered,  and  only  those 
corresponding  in  depth  and  width  should  be  used  in  the  same  course. 
The  better  method  would  be  to  gauge  the  blocks  at  the  quarry. 
This  would  lessen  the  cost  considerably ;  it  would  also  avoid  the  in- 
convenience to  the  public  due  to  the  stopping  of  travel  because  of  the 
rejection  of  defective  material  on  the  ground.  This  method  would 
undoubtedly  be  preferable  to  the  contractor,  who  would  be  saved  the 
expense  of  handling  unsatisfactory  material ;  and  it  would  also  leave 
the  inspectors  free  to  pay  more  attention  to  the  manner  in  which  the 
work  of  paving  is  performed. 

The  accurate  gauging  of  the  blocks  is  a  matter  of  much  impor- 
tance. If  good  work  is  to  be  executed,  the  blocks,  when  laid,  must  be 
in  parallel  and  even  courses;  and  if  the  blocks  be  not  accurately  gauged 
to  one  uniform  size,  the  result  will  be  a  badly  paved  street,  with  the 
courses  running  unevenly.  The  cost  of  assorting  blocks  into  lots  of 
uniform  width,  after  delivery  on  the  street,  is  far  in  excess  of  any  ad- 
ditional price  which  would  have  to  be  paid  for  accurate  gauging  at  the 
quarry. 

Foundation.  The  foundation  of  the  blocks  must  be  solid  and 
unyielding.  A  bed  of  hydraulic-cement  concrete  is  the  most  suitable, 
the  thickness  of  which  must  be  regulated  according  to  the  traffic ;  the 
thickness,  however,  should  not  be  less  than  4  inches,  and  need  not  be 
more  than  9  inches.  A  thickness  of  6  inches  will  sustain  traffic  of  600 
tons  per  foot  of  width. 

Cushion  Coat.  Between  the  surface  of  the  concrete  and  the  base 
of  the  blocks,  there  must  be  placed  a  cushion-coat  formed  of  an  incom- 
pressible but  mobile  material,  the  particles  of  which  will  readily  adjust 
themselves  to  the  irregularities  of  the  bases  of  the  blocks  and  transfer 
the  pressure  of  the  traffic  uniformly  to  the  concrete  below.  A  layer 
of  dry,  clean  sand  1  to  2  inches  thick  forms  an  excellent  cushion-coat. 


356 


HIGHWAY  CONSTRUCTION 


Its  particles  must  be  of  such  fineness  as  to  pass  through  a  No.  8  screen; 
if  coarse  and  containing  pebbles,  they  will  not  adapt  themselves  to  the 
irregularities  of  the  bases  of  the  blocks;  hence  the  blocks  will  be  sup- 
ported at  only  a  few  points,  and  unequal  settlement  will  take  place  when 
the  pavement  is  subjected  to  the  action  of  traffic.  The  sand  must  also 
be  perfectly  free  from  moisture,  and  artificial  heat  must  be  used  to  dry 
it  if  necessary.  This  requirement  is  an  absolute  necessity.  There 
should  be  no  moisture  below  the  blocks  when  laid;  nor  should  water 
be  allowed  to  penetrate  below  the  blocks ;  if  such  happens,  the  effect  of 
frost  will  be  to  upheave  the  pavement  and  crack  the  concrete. 

Where  the  best  is  desired  without  regard  to  cost,  a  layer  half  an 
inch  thick  of  asphaltic  cement  may  be  substituted  for  the  sand,  with 
superior  and  very  satisfactory  results. 

Laying  Blocks.  The  blocks  should  be  laid  stone  to  stone,  so  that 
the  joint  may  be  of  the  least  possible  width ;  wide  joints  cause  increased 
wear  and  noise,  and  do  not  increase  the  foothold.  The  courses  should 
be  commenced  on  each  side  and  worked  toward  the  middle;  and  the 
last  stone  should  fit  tightly. 

Ramming.  After  the  blocks  have  been  set,  they  should  be  well 
rammed  down;  and  the  stones  which  sink  below  the  general  level 
should  be  taken  up  and  replaced  with  a  deeper  stone  or  brought  to 
level  by  increasing  the  sand  bedding. 

The  practice  of  workmen  is  invariably  to  use  the  rammer  so  as  to 
secure  a  fair  surface.  This  is  not  the  result  intended  to  be  secured, 
but  to  bring  each  block  to  an  unyielding  bearing.  The  result  of  such 
a  surfacing  process  is  to  produce  an  unsightly  and  uneven  roadway 
when  the  pressure  of  traffic  is  brought  upon  it.  The  rammer  used 
should  weigh  not  less  than  50  pounds  and  have  a  diameter  of  not  less 
than  3  inches. 

Joint  Filling.  All  stone  block  pavements  depend  for  their  water- 
proof qualities  upon  the  character  of  the  joint  filling.  Joints  filled 
with  sand  and  gravel  are  of  course  pervious.  A  grout  of  lime  or  cement 
mortar  does  not  make  a  permanently  waterproof  joint;  it  becomes 
disintegrated  under  the  vibration  of  traffic.  An  impervious  joint  can 
be  made  only  by  employing  a  filling  made  from  bituminous  or  asphaltic 
material;  this  renders  the  pavement  more  impervious  to  moisture, 
makes  it  less  noisy,  and  adds  considerably  to  its  strength. 

Bituminous  Cement  for  Joint  Filling.    The  bituminous  materials 


857 


90  HIGHWAY  CONSTRUCTION 


employed  are:  (1)  The  tar  produced  in  the  manufacture  of  gas, 
which,  when  redistilled,  is  called  distillate,  and  is  numbered  1,  2,  3,  4, 
etc.,  according  to  its  density;  this,  material  under  the  name  of  paving- 
pitch  is  extensively  used,  both  alone  and  in  combination  with  other 
bituminous  substances;  (2)  Combinations  of  gas  tar  or  coal  tar  with 
refined  asphaltum;  (3)  Mixtures  of  refined  asphaltum,  creosote,  and 
coal  tar. 

The  formula  for  the  bituminous  joint  filling  used  in  New  York 
City,  is: 

Refined  Trinidad  asphaltum 20  parts. 

No.  4  coal-tar  distillate 100  parts. 

Residuum  of  petroleum 3  parts. 

In  Washington,  D.  C.,  coal  tar  distillate  No.  6  is  used  alone. 

In  Europe  a  bituminous  cement  much  used  is  composed  of  coal- 
tar,  asphaltum,  gas  tar,  and  creosote  oil,  in  the  proportion  of  100 
pounds  of  asphaltum  to  4  gallons  of  tar  and  1  gallon  of  creosote. 
These  proportions  are  varied  somewhat,  according  to  the  quality  of  the 
asphaltum  employed.  The  mixture  is  melted,  and  is  boiled  from 
one  to  two  hours  in  a  suitable  boiler,  being  then  poured  into  the  joints 
in  a  boiling  state.  This  mixture  is  impervious  to  moisture,  and  pos- 
sesses a  degree  of  elasticity  sufficient  to  prevent  it  from  cracking. 

The  mode  of  applying  the  bituminous  cement  is  as  follows :  After 
the  blocks  are  rammed,  the  joints  are  filled  to  a  depth  of  about  two 
inches  with  clean  gravel  heated  to  a  temperature  of  about  250°  F. ; 
then  the  hot  cement  is  poured  in  until  it  forms  a  layer  of  about  one  inch 
on  top  of  the  gravel;  then  more  gravel  is  filled  in  to  a  depth  of  about 
two  inches;  then  cement  is  poured  in  until  it  appears  on  top  of  the 
gravel,  more  gravel  being  next  added  until  it  reaches  to  within  half  an 
inch  of  the  top  of  the  blocks;  this  remaining  half-inch  is  filled  with 
cement,  and  then  fine  gravel  or  sand  is  sprinkled  over  the  joints. 

In  some  cases  the  joints  are  first  filled  with  heated  gravel;  the 
cement  is  poured  in  until  the  sand  beneath  and  the  gravel  between 
the  blocks  will  absorb  no  more,  and  the  joints  are  filled  flush  with  the 
top  of  the  pavement.  This  method  is  open  to  objection;  for,  if  the 
gravel  is  not  sufficiently  hot,  the  cement  will  be  chilled  and  will  not  flow 
to  the  bottom  of  the  joint,  but,  instead,  will  form  a  thin  layer  near  the 
surface,  which  under  the  action  of  frost  and  the  vibration  of  traffic, 
will  be  quickly  cracked  and  broken  up;  the  gravel  will  settle,  and  the 


358 


A  GOOD  EXAMPLE  OF  ROAD-BUILDING  ON  A  STEEP,  ROCKY  HILLSIDE 
View  near  Eide,  on  Hardanger  Fjord,  Norway. 


HIGHWAY  CONSTRUCTION 


91 


blocks  will  be  jarred  loose,  the  surface  of  the  pavement  becoming  a 
series  of  ridges  and  hollows. 

The  quantity  of  cement  required  per  square  yard  of  pavement  will 
vary  according  to  the  shape  of  the  blocks,  the  width  of  the  joints,  and 
the  depth  of  the  sand  bed.  With  well-shaped  blocks,  close  joints,  and 
a  half-inch  sand  bed,  the  quantity  will  vary  from  3\  to  5  gallons;  with 
ill-shaped  blocks,  wide  joints,  and  a  heavy  sand  bed,  10  to  12  gallons 


Fig.  57. 

would  not  be  an  excessive  amount  to  use  to  secure  the  result  obtained 
by  employing  well-shaped  blocks  and  close  joints. 

Stone  Pavement  on  Steep  Grades.  Stone  blocks  may  be  em- 
ployed on  all  practicable  grades;  but  on  grades  exceeding  10  per  cent, 
cobblestones  afford  a  better  foothold  than  blocks.  The  cobblestones 
should  be  of  uniform  length,  the  length  being  at  least  twice  the  breadth 
— say  stones  6  inches  long  and  1\  to  3  inches  in  diameter.  These 
should  be  set  on  a  concrete  foundation,  laid  stone  to  stone,  and  the 


Fig.  58. 

interstices  filler!  with  cement  grout  or  bituminous  cement;  or  a  bitu- 
minous concrete  foundation  may  be  employed  and  the  interstices  be- 
tween the  stones  filled  with  asphaltic  paving  cement.  Should  stone 
blocks  be  preferred,  they  must  be  laid,  when  the  grade  exceeds  5  per 
cent,  with  a  serrated  surface,  by  either  of  the  methods  shown  in  Figs. 
57  and  58.  The  method  shown  in  Fig.  57  consists  in  slightly  tilting 
the  blocks  on  their  bed  so  as  to  form  a  series  of  ledges  or  steps,  against 
which  the  horses'  feet  being  planted,  a  secure  foothold  is  obtained. 
The  method  shown  in  Fig.  58  consists  in  placing  between  the  rows  of 


350 


92  HIGHWAY  CONSTRUCTION 


stones  a  course  of  slate,  or  strips  of  creosoted  wood,  rather  less  than 
one  inch  in  thickness  and  about  an  inch  less  in  depth  than  the  blocks; 
or  the  blocks  may  be  spaced  about  one  inch  apart,  and  the  joints  filled 
with  a  grout  composed  of  gravel  and  cement.  The  pebbles  of  the 
gravel  should  vary  in  size  between  one-quarter  and  three-quarters  of 
an  inch. 

BRICK   PAVEMENTS 

Characteristics  of  Brick  Suitable  for  Paving.    These  are: 

(1)  Not  to  be  acted  upon  by  acids. 

(2)  Not  to  absorb  more  than  1-600  of  its  weight  of  water  in 
48  hours. 

(3)  Not  susceptible  to  polish. 

(4)  Rough  to  the  touch,  resembling  fine  sandpaper. 

(5)  To  give  a  clear,  ringing  sound  when  struck  together. 

(0)  When  broken,  to  show  a  compact,  uniform,  close-grained, 
structure,  free  from  air-holes  and  pebbles. 

(7)  Not  to  scale,  spall,  or  chip  when  quickly  struck  on  the  edges. 

(8)  Hard  but  not  brittle. 

Tests  of  Paving  Brick.  To  ascertain  the  quality  of  paving  brick, 
they  are  generally  subjected  to  four  tests,  namely:  (1)  Abrasion  by 
impact  (commonly  called  the  "Rattler"  test);  (2)  absorption;  (3) 
transverse  or  cross-breaking ;  (4)  crushing.  With  a  view  to  securing 
uniformity  in  the  methods  of  making  the  above  tests,  the  National 
Brick  Manufacturers'  Association  has  adopted  and  recommends  the 
following: 

Rattler  Test 

1.  Dimensions  of  the  Machine.  The  standard  machine  shall 
be  28  inches  in  diameter  and  20  inches  in  length,  measured  inside  the 
chamber. 

Other  machines  may  be  used,  varying  in  diameter  between  20  and 
30  inches,  and  in  length  between  18  and  24  inches;  but  if  this  is  done, 
a  record  of  it  must  be  attached  to  the  official  report.  I^ong  rattlers 
may  be  cut  up  into  sections  of  suitable  length  by  the  insertion  of  an 
iron  diaphragm  at  the  proper  point. 

2  Construction  of  the  Machine.  The  barrel  shall  be  supporterl 
on  trunnions  at  either  end;  in  no  case  shall  a  shaft  pass  through  the 
rattling  chamber.  The  cross-section  of  the  barrel  shall  be  a  regular 
polygon  having  14  sides.  The  heads  shall  be  composed  of  gray  cast- 


36O 


HIGHWAY  CONSTRUCTION  93 

iron,  not  chilled  or  case-hardened.  The  staves  shall  preferably  be 
composed  of  steel  plates,  since  cast-iron  peans  and  ultimately  breaks 
under  the  wearing  action  on  the  inside.  There  shall  be  a  space  of  one- 
fourth  of  an  inch  between  the  staves,  for  the  escape  of  dust  and  small 
pieces  of  waste.  Other  machines  may  be  used,  having  from  twelve  to 
sixteen  staves;  but  if  this  is  done,  a  record  of  it  must  be  attached  to 
the  official  report  of  the  test. 

3.  Composition  of  the  Charge.     All  tests  must  be  executed  on 
charges  containing  but  one  make  of  brick  or  block  at  a  time.     The 
charge  shall  consist  of  9  paving  blocks  or  12  paving  bricks,  together 
with  300  pounds  of  shot  made  of  ordinary  machinery  cast-iron.     This 
shot  shall  be  of  two  sizes,  as  described  below;  and  the  shot  charge  shall 
be  composed  one-fourth  (75  pounds)  of  the  larger  size,  and  three- 
fourths  (225  pounds)  of  the  smaller  size. 

4.  Size  of  the  Shot.     The  larger  size  shall  weigh  about  1\  pound's 
and  be  about  1\  inches  square  and  4i  inches  long,  with  slightly  round- 
ed edges.     The  smaller  size  shall  be  cubes  of  H  inches  on  a  side,  with 
rounded  edges.     The  individual  shot  shall  be  replaced  by  new  .ones 
when  they  have  lost  one-tenth  of  their  original  weight. 

5.  Revolutions  of  the  Charge.     The  number  of  revolutions  of  a 
standard  test  shall  be  1,800;  and  the  speed  of  rotation  shall  not  fall 
below  28  nor  exceed  30  revolutions  per  minute.     The  belt-power  shall 
be  sufficient  to  rotate  the  rattler  at  the  same  speed,  whether  charged 
or  empty. 

6.  Condition  of  the  Charge.     The  bricks  composing  a  charge 
shall  be  thoroughly  dried  before  making  the  test. 

7.  Calculation  of  the  Results.     The  loss  shall  be  calculated  in 
per  cents  of  the  weight  of  the  dry  brick  composing  the  charge;  and  no 
result  shall  be  considered  as  official  unless  it  is  the  average  of  two 
distinct  and  complete  tests  made  on  separate  charges  of  brick. 

Absorption  Test 

1.  The  number  of  bricks  for  a  standard  test  shall  be  five. 

2.  The  test  must  be  conducted  on  rattled  brick.     If  none  such 
are  available,  the  whole  brick  must  be  broken  in  halves  before  treatment. 

3.  Dry  the  bricks  for  48  hours  at  a  temperature  ranging  from 
230°  to  250°  F.  before  weighing  for  the  official  dry  weight. 

4.  Soak  for  48  hours  completely  immersed  in  pure  water. 


361 


94  HIGHWAY  CONSTRUCTION 


5.  After  soaking,  and  before  weighing,  the  bricks  must  be  wiped 
dry  from  surplus  water. 

6.  The  difference  in  the  weight  must  be  determined  on  scales 
sensitive  to  one  gram. 

7.  The  increase  in  weight  due  to  water  absorbed  shall  be  ca;- 
culated  in  per  cents  of  the  initial  dry  weight. 

Cross=Breaking  Test 

1.  Support  the  brick  on  edge,  or  as  laid  in  the  pavement,  on 
hardened  steel  knife-edges,  rounded  longitudinally  to  a  radius  of 
twelve  inches  and  transversely  to  a  radius  of  one-eighth  inch,  and 
bolted  in  position  so  as  to  secure  a  span  of  six  inches. 

2.  Apply  the  load  to  the  middle  of  the  top  face  through  a  hard- 
ened steel  knife-edge,  straight  longitudinally  and  rounded  transversely 
to  a  radius  of  one-sixteenth  inch. 

3.  Apply  the  load  at  a  uniform  rate  of  increase  till  fracture 
ensues. 

4.  Compute  the  modulus  of  rupture  by  the  formula 

.3wl_ 
'      2bd2' 

in  which  /  =  modulus  of  rupture,  in  pounds  per  square  inch; 
w  =  total  breaking  load,  in  pounds; 
/  =  length  of  span,  in  inches  =  0; 
/;  =  breadth  of  brick,  in  inches- 
d  =  depth  of  brick,  in  inches. 

5.  Samples  for  test  must  be  free  from  all  visible  irregularities  of 
surface  or  deformities  of  shape,  and  their  upper  and  lower  faces  must 
be  practically  parallel. 

6.  Not  less  than  ten  brick  shall  be  broken,  and  the  average  of  all 
shall  be  taken  for  a  standard  test. 

Crushing  Test 

1.  The  crushing  test  should  be  made  on  half-bricks,  loaded 
edgewise,  or  as  they  are  laid  in  the  street.     If  the  machine  used  is 
unable  to  crush  a  full  half-brick,  the  area  may  be  reduced  by  chipping 
off,  keeping  the  form  of  the  piece  to  be  tested  as  nearly  prismatic  as 
possible.     A  machine  of  at  least  100,000  pounds'  capacity  should  be 
used;  and  the  specimen  should  not  be  reduced  below  four  square 
inches  of  area  in  cross-section  at  right  angles  to  direction  of  load. 

2.  The  upper  and  lower  surfaces  should  preferably  be  ground  to 


si 

2  o 


HIGHWAY  CONSTRUCTION  95 

true  and  parallel  planes.  If  this  is  not  done,  they  should  be  bedded, 
while  in  the  testing  machine,  in  plaster  of  Paris,  which  should  be 
allowed  to  harden  ten  minutes  under  weight  of  the  crushing  planes 
only,  before  the  load  is  applied. 

3.  The  load  should  be  applied  at  a  uniform  rate  of  increase  to 
the  point  of  rupture. 

4.  Not  less  than  an  average  obtained  from  five  tests  on  five 
different  bricks  shall  constitute  a  standard  test. 

Properties  of  Paving  Bricks.  Paving  bricks  range  in  weight 
from  5J  to  1\  pounds;  in  specific  gravity,  from  1.91  to  2.70;  in  resist- 
ance to  crushing,  from  7,000  to  18,000  pounds  per  square  inch;  in 
resistance  to  cross-breaking,  R  =  1,400  to  2,000  pounds ;  in  absorption, 
from  0.15  to  3  per  cent  in  24  hours.  The  dimensions  vary  according  to 
locality  and  the  requirements  of  the  specifications.  The  "standard" 
bricks  are  2^  X  4  X  8  inches,  requiring  58  bricks  to  the  square  yard, 
and  weighing  7  pounds  each; "repressed", 2 \  X  4  X8^>  inches,  requir- 
ing 61  to  the  square  yard,  and  weighing  6i  pounds  each;  "Metropoli- 
tan", 3X4X9  inches,  requiring  45  to  the  square  yard,  and  weighing 
9\  pounds  each. 

Advantages  of  Brick  Pavements.  These  may  be  stated  as  follows : 

(1)  Ease  of  traction. 

(2)  Good  foothold  for  horses. 

(3)  Not  disagreeably   noisy. 

(4)  Yields  but  little  dust  and  mud. 

(5)  Adapted  to  all  grades. 

(6)  Easily  repaired. 

(7)  Easily  cleaned. 

(8)  But  slightly  absorbent. 

(9)  Pleasing,  to  the  eye. 

(10)  Expeditiously  laid. 

(11)  Durable  under  moderate  traffic. 

Defects  of  Brick  Pavements.  The  principal  defects  of  brick 
pavements  arise  from  lack  of  uniformity  in  the  quality  of  the  bricks, 
and  from  the  liability  of  incorporating  in  the  pavement  bricks  of  too 
soft  or  porous  a  structure,  which  crumbles  under  the  action  of  traffic 
or  frost. 

Foundation.  A  brick  pavement  should  have  a  firm  foundation. 
As  the  surface  is  made  up  of  small,  independent  blocks,  each  one  must 


96  HIGHWAY  CONSTRUCTION 


be  adequately  supported,  or  the  load  coming  upon  it  may  force  it 
downwards  and  cause  unevenness,  a  condition  which  conduces  to  the 
rapid  destruction  of  the  pavement.  Several  forms  of  foundation  have 
been  used— such  as  gravel,  plank,  sand,  broken  stone,  and  concrete. 
The  last  mentioned  is  doubtless  the  best. 

Sand  Cushion.  The  sand  cushion  is  a  layer  of  sand  placed  on 
top  of  the  concrete  to  form  a  bed  for  the  brick.  Practice  regarding 
the  depth  of  this  layer  of  sand  varies  considerably.  In  some  cases  it 
is  only  half  an  inch  deep,  varying  from  this  up  to  three  inches.  The 
sand  cushion  is  very  desirable,  as  it  not  only  forms  a  perfectly  true  and 
even  surface  upon  which  to  place  brick,  but  also  makes  the  pavement 
less  hard  and  rigid  than  would  be  the  case  were  the  brick  laid  directly 
on  the  concrete. 

The  sand  is  spread  evenly,  sprinkled  with  water,  smoothed,  and 
brought  to  the  proper  contour  by  screeds  or  wooden  templets,  properly 
trussed,  mounted  on  wheels  or  shoes  which  bear  upon  the  upper  sur- 
face of  the  curb.  Moving  the  templet  forward  levels  and  forms  the 
sand  to  a  uniform  surface  and  proper  shape. 

The  sand  used  for  the  cushion-coat  should  be  clean  and  free  from 
loam,  moderately  coarse,  and  free  from  pebbles  exceeding  one-quarter 
inch  in  size. 

Manner  of  Laying.  The  bricks  should  be  laid  oh  edge,  as  closely 
and  compactly  as  possible,  in  straight  courses  across  the  street,  with 
the  length  of  the  bricks  at  right  angles  to  the  axis  of  the  street.  Joints 
should  be  broken  by  at  least  3  inches.  None  but  whole  bricks  should 
be  used,  except  in  starting  a  course  or  making  a  closure.  To  provide 
for  the  expansion  of  the  pavement,  both  longitudinal  and  transverse 
expansion-joints  are  used,  the  former  being  made  by  placing  a  board 
templet  seven-eighths  of  an  inch  thick  against  the  curb  and  abutting 
the  brick  thereto.  The  transverse  joints  are  formed  at  intervals 
varying  between  25  and  50  feet,  by  placing  a  templet  or  building-lath 
three-eighths  of  an  inch  thick  between  two  or  three  rows  of  brick. 
After  the  bricks  are  rammed  and  ready  for  grouting,  these  templets  are 
removed,  and  the  spaces  so  left  are  rilled  with  coal-tar  pitch  or  asphal- 
tic  paving  cement.  The  amount  of  pitch  or  cement  required  will  vary 
between  one  and  one  and  a-half  pounds  per  square  yard  of  pavement, 
depending  upon  the  width  of  the  joints.  After  25  or  30  feet  of  the 
pavement  is  laid,  every  part  of  it  should  be  rammed  with  a  rammer 


364 


HIGHWAY  CONSTRUCTION 


weighing  not  less  than  50  pounds;  and  the  bricks  which  sink  below  the 
general  level  should  be  removed,  sufficient  sand  being  added  to  raise 
the  brick  to  the  required  level.  After  all  objectionable  brick  have 
been  removed,  the  surface  should  be  swept  clean,  then  rolled  with  a 
steam  roller  weighing  from  3  to  6  tons.  The  object  of  rolling  is  to 
bring  the  bricks  to  an  unyielding  bearing  with  a  plane  surface;  if  this 
is  not  done,  the  pavement  will  be  rough  and  noisy  and  will  lack  dura- 


bility. The  rolling  should  be  first  executed  longitudinally,  beginning 
at  the  crown  and  working  toward  the  gutter,  taking  care  that  each 
return  trip  of  the  roller  covers  exactly  the  same  area  as  the  preceding 
trip,  so  that  the  second  passage  may  neutralize  any  careening  of  the 
brick  due  to  the  first  passage. 

The  manner  of  laying  brick  at  street  intersections  is  shown  in 
Fig.  59. 


365 


98  HIGHWAY  CONSTRUCTION 


Joint  Filling.  The  character  of  the  material  used  in  filling  the 
joints  between  the  brick  has  considerable  influence  on  the  success  and 
durability  of  the  pavement.  Various  materials  have  been  used — such 
as  sand,  coal-tar  pitch,  asphalt,  mixtures  of  coal-tar  and  asphalt,  and 
Portland  cement,  besides  various  patented  fillers;  as  "Murphy's 
grout",  which  is  made  from  ground  slag  and  cement.  Each  material 
has  its  advocates,  and  there  is  much  difference  of  opinion  as  to  which 
gives  the  best  results. 

The  best  results  seem  to  be  obtained  by  using  a  high  grade  of 
Portland  cement  containing  the  smallest  amount  of  lime  in  its  composi- 
tion, the  presence  of  the  lime  increasing  the  tendency  of  the  filler  to 
swell  through  absorption  of  moisture,  causing  the  pavement  to  rise 
or  to  be  lifted  away  from  its  foundation,  and  thus  producing  the  roaring 
or  rumbling  noise  so  frequently  complained  of. 

The  Portland  cement  grout,  when  uniformly  mixed  and  carefully 
placed,  resists  the  impact  of  traffic  and  wears  well  with  brick.  When  a 
failure  occurs/repairs  can  be  made  quickly;  and,  if  made  early,  the 
pavement  will  be  restored  to  a  good  condition.  If,  however,  repairs 
are  neglected,  the  brick  soon  loosens  and  the  pavement  fails. 

The  office  of  a  filler  is  to  prevent  water  from  reaching  the  founda- 
tion, and  to  protect  the  edges  of  the  brick  from  spalling  under  traffic. 
In  order  to  meet  both  of  these  requirements,  every  joint  must  be  filled 
to  the  top,  and  must  remain  so,  wearing  down  with  the  brick.  Sand 
does  not  meet  these  requirements.  Although  at  first  making  a  good 
filler,  being  inexpensive  and  reducing  the  liability  of  the  pavement  to 
be  noisy,  it  soon  washes  out,  leaving  the  edges  of  the  brick  unprotected 
and  consequently  liable  to  be  chipped.  Coal-tar  and  the  mixtures  of 
coal-tar  and  asphalt  have  an  advantage  in  rendering  a  pavement  less 
noisy  and  in  cementing  together  any  breaks  that  may  occur  through 
upheavals  from  frost  or  other  causes;  but,  unless  made  very  hard,  they 
have  the  disadvantage  of  becoming  soft  in  hot  weather  and  flowing 
to  the  gutters  and  low  places  in  the  pavement,  there  forming  a  black 
and  unsightly  scale  and  leaving  the  high  parts  unprotected.  The 
joints,  thus  deprived  of  their  filling,  become  receptacles  for  water,  mud, 
and  ice  in  turn;  and  the  edges  of  the  brick  are  quickly  broken  down. 
Some  of  these  mixtures  become  so  brittle  in  winter  that  they  crack 
and  fly  out  of  the  joints  under  the  action  of  traffic. 

The  Portland  cement  filler  is  prepared  by  mixing  two  parts  of 


366 


HIGHWAY  CONSTRUCTION 


cement  and  one  part  of  fine  sand  with  sufficient  water  to  make. a  thin 
grout.  The  most  convenient  arrangement  for  preparing  and  dis- 
tributing the  grout  is  a  water-tight  wooden  box  carried  on  four  wooden 
wheels  about  12  inches  in  diameter.  The  box  may  be  about  4  feet 
wide,  7  feet  long,  and  12  inches  deep,  furnished  with  a  gate  about  8 
inches  wide,  in  the  rear  end.  The  box  should  be  mounted  on  the 
wheels  with  an  inclination,  so  that  the  rear  end  is  about. 4  inches  lower 
than  the  front  end. 

The  operation  of  placing  the  filler  is  as  follows :  The  cement  and 
sand  are  placed  in  the  box,  and  sufficient  water  is  added  to  make  a 
thin  grout.  The  box  is  located  about  12  feet  from  the  gutter,  the  end 
gate  opened,  and  about  2 -cubic  feet  of  the  grout  allowed  to  flow  out 
and  run  over  the  top  of  the  brick  (care  being  taken  to  stir  the  grout 
while  it  is  being  discharged).  If  the  brick  are  very  dry,  the  entire 
surface  of  the  pavement  should  be  thoroughly  wet  with  a  hose  before 
applying  the  grout;  if  not,  absorption  of  the  water  from  the  grout  by 
the  bricks  will  prevent  adhesion  between  the  bricks  and  the  cement 
grcut.  The  grout  is  swept  into  the  joints  by  ordinary  bass  brooms. 
After  about  100  feet  in  length  of  the  pavement  has  been  covered  the 
box  is  returned  to  the  starting-point,  and  the  operation  is  repeated 
with  a  grout  somewhat  thicker  than  the  first.  If  this  second  applica- 
tion is  not  sufficient  to  fill  the  joints,  the  operation  is  repeated  as  often 
as  may  be  necessary  to  fill  them.  If  the  grout  has  been  made  too  thin, 
or  the  grade  of  the  street  is  so  great  that  the  grout  will  not  remain  long 
enough  in  place  to  set,  dry  cement  may  be  sprinkled  over  the  joints  and 
swept  in.  After  the  joints  are  completely  filled  and  inspected,  allowing 
three  or  four  hours  to  intervene,  the  completed  pavement  should  be 
covered  with  sand  to  a  depth  of  about  half  an  inch,  and  the  roadway 
barricaded,  and  no  traffic  allowed  on  it  for  at  least  ten  days. 

The  object  of  covering  the  pavement  with  sand  is  to  prevent  the 
grout  from  drying  or  settling  too  rapidly;  hence,  in  dry  and  windy 
weather,  it  should  be  sprinkled  from  time  to  time.  If  coarse  sand  is 
employed  in  the  grout,  it  will  separate  from  the  cement  during  the 
operation  of  filling  the  joints,  with  the  result  that  many  joints  will  be 
filled  with  sand  and  very  little  cement,  while  others  will  be  filled  with 
cement  and  little  or  no  sand ;  thus  there  will  be  many  spots  in  the  pave- 
ment in  which  no  bond  is  foimed  between  the  bricks,  and  under  the 
action  of  traffic  these  portions  will  quickly  become  defective. 


367 


100  HIGHWAY  CONSTRUCTION 

The  coal-tar  filler  is  best  applied  by  pouring  the  material  from 
buckets,  And  brooming  it  into  the  joints  with  wire  brooms.  In  order  to 
fill  the  joints  effectually,  it  must  be  used  only  when  very  hot.  To 
secure  this  condition,  a  heating  tank  on  wheels  is  necessary.  It  should 
have  a  capacity  of  at  least  five  barrels,  and  be  kept  at  a  uniform  tem- 
perature all  day.  One  man  is  necessary  to  feed  the  fire  and  draw  the 
material  into  the  buckets;  another,  to  carry  the  buckets  from  the  heat- 
ing-tank to  a  third,  who  pours  the  material  over  the  street.  The  latter 
starts  to  pour  in  the  center  of  the  street,  working  backward  toward  the 
curb,  and  pouring  a  strip  about  two  feet  in  width.  A  fourth  man, 
with  a  wire  broom,  follows  immediately  after  him,  sweeping  the  sur- 
plus material  toward  the  pourer  and  in  the  direction  of  the  curb.  This 
method  leaves  the  entire  surface  of  the  pavement  covered  with  a  thin 
coating  of  pitch,  which  should  immediately  be  covered  with  a  light 
coating  of  sand ;  the  sand  becomes  imbedded  in  the  pitch.  Under  the 
action  of  traffic,  this  thin  coating  is  quickly  worn  away,  leaving  the 
surface  of  the  bricks  clean  and  smooth. 

Tools  Employed  in  Construction  of  Block  Pavements.  The 
principal  tools  required  in  constructing  block  pavements  comprise 
hammers  and  rammers  of  varying  sizes  and  shapes,  depending  on  the 
material  and  size  of  the  blocks  to  be  laid;  also  crowbars,  sand  screens, 
an:!  rattan  and  wire  brooms.  Cobblestones,  square  blocks,  and  brick 
require  different  types  of  both  hammers  and  rammers  for  adjusting 
them  to  place  and  forcing  them  to  their  seat.  A  cobblestone  rammer, 
for  example,  is  usually  made  of  wrood  (generally  locust)  in  the  shape  of 
a  long  truncated  cone,  banded  with  iron  at  top  and  bottom,  weighing 
about  40  pounds,  and  having  two  handles,  o;ie  at  the  top  and  another 
'on  one  side.  A  Belgian  block  rammer  is  slightly  heavier,  consisting 
of  an  upper  part  of  wood  set  in  a  steel  base;  while  a  rammer  for  granite 
blocks  is  still  heavier,  comprising  an  iron  base  with  cast-steel  face,  into 
which  is  set  a  locust  plug  with  hickory  handles.  For  laying  brick,  a 
wooden  rammer  shod  with  cast  iron  or  steel  and  weighing  about  27 
pounds  is  used.  A  light  rammer  of  about  20  pounds'  weight,  consist' 
ing  of  a  metallic  base  attached  to  a  long,  slim  wooden  handle,  is  used 
for  miscellaneous  work,  such  as  tamping  in  trenches,  next  to  curbs,  etc. 

Concrete=Mixing  Machine.  Where  large  quantities  of  concrete 
are  required,  as  in  the  foundations  of  improved  pavements,  concrete 
can  be  prepared  more  expeditiously  and  economically  by  the  use  of 


868 


HIGHWAY  CONSTRUCTION 


101 


mechanical  mixers,  and  the  ingredients  will  be  more  thoroughly  mixed, 
than  by  hand.  Thorough  incorporation  of  the  ingredients  is  an  essen- 
tial element  in  the  quality  of  a  concrete.  When  mixed  by  hand,  how- 
ever, the  incorporation  is  rarely  complete,  because  it  depends  upon  the 
proper  manipulation  of  the  hoe  and  shovel.  The  manipulation, 
although  extremely  simple,  is  rarely  performed  by  the  ordinary  laborer 
unless  he  is  constantly  watched  by  the  overseer. 

Several  varieties  of  concrete-mixing  machines  are  in  the  market. 
A  convenient  portable  type  is  illustrated  in  Fig.  60.     The  capacity  of 


Fig.  60.    Concrete  Mixing  Mat-blue. 


the  mixers  ranges  from  five  to  twenty  cubic  yards  per  hour,  de-lending 
upon  size,  regularity  with  which  the  materials  are  supplied,  speed,  etc. 

Gravel  Heaters.  Fig.  61  illustrates  a  device  commonly  employed 
for  heating  the  gravel  used  for  joint  filling  in  stone-block  pavements. 
These  heaters  are  made  in  various  sizes,  a  common  size  being  9  feet 
long,  5  feet  wide,  and  3  feet  9  inches  high. 

Melting  Furnaces,  for  heating  the  pitch  or  tar  for  joint  filling,  are 
illustrated  by  Fig.  62.     Various  sizes  are  on  the  market. 
WOOD  PAVEMENTS 

Wood  pavements  are  formed  of  either  rectangular  or  cylindrical 
blocks  of  wood.  The  rectangular  blocks  are  generally  3  inches  wide, 


102 


HIGHWAY  CONSTRUCTION 


9  inches  long,  and  6  inches  deep;  the  round  blocks  are  commonly  G 
inches  in  diameter  and  6  inches  long. 

The  kinds  of  wood  most  commonly  used  are  cedar,  cypress,  juni- 
per, yellow  pine,  and  mesquite;  and  recently  jarrah  from  Australia, 
and  pyinyado  from  India,  have  been  used. 

The  wood  is  used  in  its  natural  condition,  or  impregnated  with 
creosote  or  other  chemical  preservative. 

The  blocks  of  wood  are  laid  either -on  the  natural  soil,  on  a  bed 
of  sand  and  gravel,  on  a  layer  of  broken  stone,  on  a  layer  of  concrete, 


'nig.  62.   .Melting  Furnace. 


or,  .sometimes,  on  a  double  layer  of  plank.     The  joints  are  filled  either 
with  sand,  paving-pitch,  or  Portland-cement  grout. 

Advantages.     The  advantages  of  wood  pavement  may  be  stated 
as  follows : 

(1)  It  affords  good  foothold  for  horses. 

(2)  It  offers  less  resistance  to  traction  than  stone,  and  slightly 
more  than  asphalt. 

(3)  It  suits  all  classes  of  traffic. 

(4)  It  may  be  used  on  grades  up  to  five  per  cent. 

(5)  It  is  moderately  durable. 

(0)     It  yields  no  mud  when  laid  upon  an  impervious  foundation. 
(7)     It  yields  but  little  dust. 


370 


HIGHWAY  CONSTRUCTION  103 

(8)  It  is  moderate  in  first  cost. 

(9)  It  is  not  disagreeably  noisy. 

Defects.     The  principal  objections  to  wood  pavement  are: 

(1)  It  is  difficult  to  cleanse. 

(2)  Under  certain  conditions  of  the  atmosphere  it  becomes 
greasy  and  very  unsafe  for  horses. 

(3)  It  is  not  easy  to  open  for  the  purpose  of  gaining  access  to 
underground  pipes,  it  being  necessary  to  remove  rather  a  large  surface 
for  this  purpose,  which  has  to  be  left  a  little  time  after  being  repaired 
before  traffic  is  again  allowed  upon  it. 

(4)  It  is  absorbent  of  moisture. 

(5)  It  is  claimed  by  many  that  wood  pavements  are  unhealthy. 
Quality  of  Wood.     The  question  as  to  which  of  the  various  kinds 

of  wood  available  is  the  most  durable  and  economical,  has  not 
been  satisfactorily  determined.  Many  varieties  have  been  tried.  In 
England,  preference  is  given  to  Baltic  fir,  yellow  pine,  and  Swedish 
yellow  deal.  In  the  United  States  the  variety  most  used  (on  account 
of  its  abundance  and  cheapness)  is  cedar;  but  yellow  pine,  tamarack, 
and  mesquite  have  also  been  used  to  a  limited  extent,  and  cypress  and 
juniper  are  being  largely  used  in  some  of  the  Southern  States. 

Hardwoods,  such, as  oak,  etc.,  do  not  make  the  best  pavements,  as 
such  woods  become  slippery.  The  softer,  close-grained  woods,  such 
as  cedar  and  pine,  wear  better  and  give  good  foothold. 

The  wood  employed  should  be  sound  and  seasoned,  free  from  sap, 
shakes,  and  knots.  Defective  blocks  laid  in  the  pavement  will  quickly 
cause  holes  in  the  surface,  and  the  adjoining  blocks  will  suffer  under 
wear,  the  whole  surface  becoming  bumpy. 

Chemical  Treatment  of  Wood.  The  great  enemy  of  all  wood 
pavements  is  decay,  induced  by  the  action  of  the  air  and  water.  Wood 
is  porous,  absorbs  moisture,  and  thus  hastens  its  own  destruction. 
Many  processes  have  been  invented  to  overcome  this  defect.  The 
most  popular  processes  at  present  are  crcosoting  and  modifications  of 
the  same,  known  as  the  "creo-resinate"  and  "kreodine"  processes. 
These  consist  of  creosote  mixed  with  various  chemicals  which  are 
supposed  to  add  to  the  preserving  qualities  of  the  creosote. 

Creosoting.  This  process  consists  in  impregnating  the  wood  with 
the  oil  of  tar,  called  creosote,  from  which  the  ammonia  has  been  ex- 
pelled, the  effect  being  to  coagulate  the  albumen  and  thereby  prevent 


371 


104  HIGHWAY  CONSTRUCTION 


its  decomposition,  also  to  fill  the  pores  of  the  wood  with  a  bituminous 
substance  which  excludes  both  air  and  moisture,  and  which  is  noxious 
to  the  lower  forms  of  animal  and  vegetable  life.  In  adopting  this  pro- 
cess, all  moisture  should  be  dried  out  of  the  pores  of  the  timber.  The 
softer  woods,  while  warm  from  the  drying-house,  may  be  immersed  at 
once  in  an  open  tank  containing  hot  creosote  oil,  when  they  will  absorb 
about  8  or  9  pounds  per  cubic  foot.  For  hardwoods,  and  woods  which 
are  required  to  absorb  more  than  8  or  9  pounds  of  creosote  per  cubic 
foot,  the  timber  should  be  placed  in  an  iron  cylinder  with  closed  ends, 
and  the  creosote,  which  should  be  heated  to  a  temperature  of  about 
120°  F.,  forced  in  with  a  pressure  of  170  pounds  to  the  square  inch. 
The  heat  must  be  kept  up  until  the  process  is  complete,  to  prevent  the 
creosote  from  crystallizing  in  the  pores  of  the  wood.  By  this  means 
the  softer  woods  will  easily  absorb  from  10  to  12  pounds  of  oil  per  cubic 
foot. 

The  most  effective  method,  however,  is  to  exhaust  the  air  from  tht 
cylinder  after  the  timber  is  inserted;  then  to  allow  the  oil  to  flow  in;  and 
when  the  cylinder  is  full,  to  use  a  force  pump  with  a  pressure  of  150  to 
200  pounds  per  square  inch,  until  the  wood  has  absorbed  the  requisite 
quantity  of  oil,  as  indicated  by  a  gauge,  which  should  be  fitted  to  the 
reservoir  tank. 

The  oil  is  usually  heated  by  coils  of  pipe  placed  in  the  reservoir, 
through  which  a  current  of  steam  is  passed. 

The  quantity  of  creosote  oil  recommended  to  be  forced  into  the 
wood  is  from  8  to  12  pounds  per  cubic  foot.  Into  oak  and  other  hard 
woods  it  is  difficult  to  force,  even  with  the  greatest  pressure,  more  than 
2  or  3  pounds  of  oil. 

The  advantages  of  this  process  are :  The  chemical  constituents  of 
the  oil  preserve  the  fibers  of  the  wood  by  coagulating  the  albumen  of 
the  sap ;  the  fatty  matters  act  mechanically  by  filling  the  pores  and  thus 
exclude  water;  while  the  carbolic  acid  contained  in  the  oil  is  a  powerful 
disinfectant.  , 

The  life  of  the  wood  is  extended  by  any  of  the  above  processes,  by 
preserving  it  from  decay;  but  such  processes  have  little  or  no  effect  on 
the  wear  of  the  blocks  under  traffic. 

The  process  of  dipping  the  blocks  in  coal  tar  or  creosote  oil  is 
injurious.  Besides  affording  a  cover  for  the  use  of  defective  or  sappy 
wood,  it  hastens  decay,  especially  of  green  wood ;  it  closes  up  the  ex- 


372 


HIGHWAY  CONSTRUCTION 


105 


terior  of  the  cells  of  the  wood  so  that  moisture  cannot  escape,  thus 
causing  fermentation  to  take  place  in  the  interior  of  the  block,  which 
quickly  destroys  the  strength  of  the  fibers  and  reduces  them  to  punk. 

Expansion  of  Blocks.  Wood  blocks  expand  on  exposure  to 
moisture;  and,  when  they  are  laid  end  to  end  across  the  street,  the 
curbstones  are  liable  to  be  displaced,  or  the  courses  of  the  blocks  will 
be  bent  into  reserve  curves.  To  avoid  this,  the  joints  of  the  courses 
near  the  curb  may  be  left  open  until  expansion  has  ceased,  the  space 
being  temporarily  filled  with  sand.  The  rate  of  expansion  is  about 
1  inch  in  8  feet,  but  Caries  for  different  woods.  The  time  required  for 
the  wood  to  become  fully  expanded  varies  from  12  to  18  months.  By 
employing  blocks  impregnated  with  the  oil  of  creosote,  this  trouble  will 
be  avoided.  'Blocks  so  treated  do  not  contract  or  expand  to  any  appre- 
ciable extent. 

The  comparative  expansion  of  creosoted  and  plain  wood  blocks 
after  immersion  in  water  for  forty-eight  hours,  in  percentage  on  orig- 
inal dimensions,  was: 

Expansion  of  Wood  Paving  Blocks 


On  length  of  block.. 
On  width  "  '•  . 
On  depth  "  "  . 


Manner  of  Laying.  The  blocks  are  set  with  the  fiber  vertical, 
and  the  long  dimension  crosswise  of  the  street,  the  longitudinal  joints 
being  broken  by  a  lap  of  at  least  one-third  the  length  of  the  block;  the 


Fig.  63. 

blocks  should  be  laid  so  as  to  have  the  least  possible  width  of  joint. 
Wide  joints  hasten  the  destruction  of  the  wood  by  permitting-  the  fibers 
to  wear  under  traffic,  which  also  causes  the  surface  of  the  pavement 


373 


106  HIGHWAY  CONSTRUCTION 

to  wear  in  small  ridges.  The  most  recent  practice  for  laying  blocks 
on  3  per  cent  grades,  has  been  to  remove  from  the  top  of  one  side  of 
each  block  a  strip  £  inch  thick  and  1£  inches  deep,  extending  the  length 
of  the  block.  When  the  blocks  are  laid  and  driven  closely  together, 
there  is  a  quarter-inch  opening  or  joint  extending  clear  across  the  street 
in  each  course.  These  joints  are  filled  with  Portland  cement  grout. 
Fig.  63  shows  a  section  of  pavement  having  this  form  of  joint. 

Filling  for  Joints.  The  best  materials  for  filling  the  joints  are 
bitumen  for  the  lower  two  or  three  inches,  and  hydraulic  cement  grout 
for  the  remainder  of  the  depth.  The  cement  grout  protects  the  pitch 
from  the  action  of  the  sun,  and  does  not  wear  down  very  much  below 
the  surface  of  the  wood. 

ASPHALT  PAVEMENTS. 

Asphaltic  Paving  Materials.  All  asphaltic  or  bituminous  pave- 
ments are  composed  of  two  essential  parts — namely,  the  cementing 
material  (matrix)  and  the  resisting  material  (aggregate).  Each  has  a 
distinct  function  to  perform;  the  first  furnishes  and  preserves  the  co- 
herency of  the  mass ;  the  second  resists  the  wear  of  traffic. 

Two  classes  of  asphaltic  paving  compounds  are  in  use, — namely, 
natural  and  artificial.  The  "natural"  variety  is  composed  of  either 
limestone  or  sandstone  naturally  cemented  with  bitumen.  To  this 
class  belong  the  bituminous  limestones  of  Europe,  Texas,  Utah,  etc., 
and  the  bituminous  sandstones  of  California,  Kentucky,  Texas,  Indian 
Territory,  etc.  The  "artificial"  consists  of  mixtures  of  asphaltic 
cement  with  sand  and  stone  dust.  To  this  class  belong  the  pavements 
made  from  Trinidad,  Bermudez,  Cuban,  and  similar  asphaltums. 
For  the  artificial  variety,  most  hard  bitumens  are,  when  properly 
prepared,  equally  suitable.  For  the  aggregate,  the  most  suitable  mate- 
rials are  stone-dust  from  the  harder  rocks,  such  as  granite,  trap,  etc., 
and  sharp  angular  sand.  These  materials  should  be  entirely  free  from 
loam  and  vegetable  impurities.  The  strength  and  enduring  qualities 
of  the  mixture  will  depend  upon  the  quality,  strength,  and  proportion 
of  each  ingredient,  as  well  as  upon  the  cohesion  of  the  matrix  and  its 
adhesion  to  the  aggregate. 

Bituminous  limestone  consists  of  carbonate  of  lime  naturally 
cemented  with  bitumen  in  proportions  varying  from  80  to  93  per  cent 
of  carbonate  of  lime  and  from  7  to  20  per  cent  of  bitumen.  Its  color, 
when  freshly  broken,  is  a  dark  (almost  black)  chocolate  brown,  the 


374 


HIGHWAY  CONSTRUCTION  107 

darker  color  being  due  to  a  large  percentage  of  bitumen.  At  a  tem- 
perature of  from  55°  to  70°  F.,  the  material  is  hard  and  sonorous,  and 
breaks  easily  with  an  irregular  fracture;  at  temperatures  between  70° 
and  140°  F.  it  softens,  passing  with  the  rise  in  temperature  through 
various  degrees  of  plasticity,  until,  at  between  140°  and  160°  F.,  it 
begins  to  crumble;  at  212°  it  commences  to  melt;  and  at  280°  F.  it  is 
completely  disintegrated.  Its  specific  gravity  is  about  2.235. 

Bituminous  limestone  is  the  material  employed  for  paving  pur- 
poses throughout  Europe.  It  is  obtained  principally  from  deposits 
at  Val-de-Travers,  canton  of  Neufchatel,  Switzerland;  at  Seysell,  in 
the  Department  of  Ain,  France;  at  Ragusa,  Sicily;  at  Limmer,  near 
Hanover;  and  at  Vorwohle,  Germany. 

Bituminous  limestone  is  found  in  several  parts  of  the  United 
States.  Two  of  these  deposits  are  at  present  being  worked — one  in 
Texas,  the  material  from  which  is  called  "lithocarbon";  and  one  on  the 
Wasatch  Indian  Reservation.  These  deposits  contain  from  10  to  30 
per  cent  of  bitumen. 

The  bituminous  limestones  which  contain  about  10  per  cent  of 
bitumen  are  used  for  paving  in  their  natural  condition,  being  simply 
reduced  to  powder,  heated  until  thoroughly  softened,  then  spread  while 
hot  upon  the  foundation,  and  tamped  and  rammed  until  compacted. 

Bituminous  sandstones  are  composed  of  sandstone  rock  impreg- 
nated with  bitumen  in  amounts  varying  from  a  trace  to  70  per  cent. 
They  are  found  in  both  Europe  and  America.  In  Europe,  they  are 
chiefly  used  for  the  production  of  pure  bitumen,  which  is  extracted  by 
boiling  or  macerating  them  with  water.  In  the  United  States,  exten- 
sive deposits  are  found  in  the  Western  States;  and  since  1880  they  have 
been  gradually  coming  into  use  as  a  paving  material,  so  that  now  up- 
wards of  150  miles  of  streets  in  Western  cities  are  paved  with  them. 
They  are  prepared  for  use  as  paving  material  by  crushing  to  powder, 
which  is  heated  to  about  250°  F.  or  until  it  becomes  plastic,  then  spread 
upon  the  street  and  compressed  by  rolling;  sometimes  sand  or  gravel 
is  added,  and  it  is  stated  that  a  mixture  of  about  80  per  cent  of  gravel 
makes  a  durable  pavement. 

Trinidad  Asphaltum.  The  deposits  of  asphaltum  in  the  island 
of  Trinidad,  W.  I.,  have  been  the  main  source  of  supply  for  the  asphal- 
tum used  in  street  paving  in  the  United  States.  Three  kinds  are  found 
there,  which  have  been  named,  according  to  the  source,  lake-pitch, 


375 


108  HIGHWAY  CONSTRUCTION 

land  or  overflow  pitch,  and  iron  pitch.  The  first  and  most  valuable 
kind  is  obtained  from  the  so-called  Pitch  Lake. 

The  term  land  or  overflow  pitch  is  applied  to  the  deposits  of 
asphaltum  found  outside  the  lake.  These  deposits  form  extensive 
beds  of  variable  thickness,  and  are  covered  with  from  a  few  to  several 
feet  of  earth ;  they  are  considered  by  some  authorities  to  be  formed  from 
pitch  which  has  overflowed  from  the  lake;  by  others  to  be  of  entirely 
different  origin.  The  name  cheese  pitch  is  given  to  such  portions  of  the 
land  pitch  as  more  nearly  resemble  that  obtained  from  the  lake. 

The  term  iron  pitch  is  used  to  designate  large  and  isolated  masses 
of  extremely  hard  asphaltum  found  both  within  and  without  the  bor- 
ders of  the  lake.  It  is  supposed  to  have  been  formed  by  the  action  of 
heat  caused  by  forest  fires,  which,  sweeping  over  the  softer  pitch,  re- 
moved its  more  volatile  constituents. 

The  name  epurce  is  given  to  asphaltum  refined  on  the  island  of 
Trinidad.  The  process  is  conducted  in  a  very  crude  manner,  in  large, 
open,  cast-iron  sugar  boilers. 

The  characteristics  of  crude  Trinidad  asphaltum,  both  lake  and 
land,  are  as  follows :  It  is  composed  of  bitumen  mixed  with  fine  sand, 
clay,  and  vegetable  matter.  Its  specific  gravity  varies  according  to  the 
impurities  present,  but  is  usually  about  1.28.  Its  color,  when  fieshly 
excavated,  is  a  brown,  which  changes  to  black  on  exposure  to  the  at- 
mosphere. When  freshly  broken,  it  emits  the  usual  bituminous  odor- 
It  is  porous,  containing  gas  cavities,  and  in  consistency  resembles 
cheese.  If  left  long  enough  in  the  sun,  the  surface  will  soften  and  melt, 
and  will  finally  flow  into  a  more  or  less  compact  mass. 

Refined  Trinidad  Asphaltum.  The  crude  asphaltum  is  refined 
or  purified  by  melting  it  in  iron  kettles  or  stills  by  the  application  of 
indirect  heat. 

The  operation  of  refining  proceeds  as  follows :  During  the  heat- 
ing, the  water  and  lighter  oils  are  evaporated;  the  asphaltum  is  lique- 
fied; the  vegetable  matter  rises  to  the  surface,  and  is  skimmed  off;  the 
earthy  and  siliceous  matters  settle  to  the  bottom;  and  the  liquid  asphal- 
tum is  drawn  off  into  old  cement  or  flour  barrels. 

When  the  asphaltum  is  refined  without  agitation,  the  residue 
remaining  in  the  still  forms  a  considerable  percentage  of  the  crude 
material,  frequently  amounting  to  12  per  cent;  and  it  was  at  one  time 
considered  that  the  greater  the  amount  of  this  residue  the  better  the 


376 


HIGHWAY  CONSTRUCTION 


109 


quality  of  the  refined  asphaltum.  Since  agitation  has  been  adopted, 
however,  the  greater  part  of  the  earthy  and  siliceous  matters  is  retained 
in  suspension;  and  it  has  come  to  be  considered  just  as  desirable  for 
a  part  of  the  surface  mixture  as  the  sand  which  is  subsequently  added. 
The  refined  asphaltum,  if  for  local  use,  is  generally  converted  into 
cement  in  the  same  still  in  which  it  was  refined. 

The  average  composition  of  both  the  land  and  lake  varieties  is 
shown  by  the  following    analyses : 

Average  Composition  of  Trinidad  Asphaltum 


CONSTITUENTS 

LAKE 

LAND 

Hard 

Soft 

Per  Cent 

07  ^5 

Per  Cent 
34.10 
25.05 
6.85 
34.50 

Per  Cent 
26.62 
27.57 
8.05 
37.76 

Inorganic  matter  
Organic  non-bituminous  matter 

26.  H8 
7.63 
38.14 

Bitumen 

When  the  analyses  are  calculated  to  a  basis  of  dry 
substances,  the  composition  is:  Inorganic  matter 
Organic  matter  not  bitumen 

100.00 

100.00 

38.00 
9.64 
52.36 

100.00 

36.56 

10.57 
52.87 

37.74 
10.68 
51.58 

Bitumen  

The  substances  volatilized  in  10  hours  at  400°  F  .  .. 
The  substances  soften  at  

100.00 

100.00 

100.00 

3.66 

190°  F. 
200°  F. 

12.24 
170°  F. 
185°  F. 

0.86  to  1.37 
200°  to  2503  F. 
2  10°  to  328°  F. 

flow  at  

The  characteristics  of  refined  Trinidad  asphaltum  are  as  follows: 
The  color  is  black,  with  a  homogeneous  appearance.  At  a  tempera- 
ture of  about  70°  F.,  it  is  very  brittle,  and  breaks  with  a  conchoidal 
fracture.  It  burns  with  a  yellowish-white  flame,  and  in  burning  emits 
an  empyreumatic  odor,  and  possesses  little  cementitious  quality.  To 
give  it  the  required  plasticity  and  tenacity,  it  is  mixed  while  liquid  with 
from  Ifi  to  21  pounds  of  residuum  oil  to  100  pounds  of  asphaltum. 

The  product  resulting  from  the  combination  is  called  asphalt 
paving-cement.  Its  consistency  should  be  such  that,  at  a  temperature 
of  from  70°  to  80°  F.,  it  can  be  easily  indented  with  the  fingers,  and  on 
slight  warming  be  drawn  out  in  strings  or  threads. 

Artificial  Asphalt  Pavements.  The  pavements  made  from  Trini- 
dad, Bermudez,  California,  and  similar  asphaltums,  are  composed  of 
mechanical  mixtures  of  asphaltic  cement,  sand,  and  stone-dust. 

The  sand  should  be  equal  in  quality  to  that  used  for  hydraulic 
cement  mortar;  it  must  be  entirely  free  from  clay,  loam,  and  vegetable 


110  HIGHWAY  CONSTRUCTION 

impurities;  its  grains  should  be  angular  and  range  from  coarse  to  fine. 

The  stone-dust  is  used  to  aid  in  filling  the  voids  in  the  sand  and 
thus  reduce  the  amount  of  cement.  The  amount  used  varies  with  the 
coarseness  of  the  sand  and  the  quality  of  the  cement,  and  ranges  from 
5  to  15  per  cent.  (The  voids  in  sand  vary  from  .3  to  .5  per  cent.) 

As  to  the  quality  of  the  stone-dust,  that  from  any  durable  stone  is 
equally  suitable.  Limestone-dust  was  originally  used,  and  has  never 
been  entirely  discarded. 

The  paving  composition  is  prepared  by  heating  the  mixed  sand 
and  stone-dust  and  the  asphalt  cement  separately  to  a  temperature  of 
about  300°  F.  The  heated  ingredients  are  measured  into  a  pu^-:nill 
and  thoroughly  incorporated.  When  this  is  accomplished,  the  mix- 
ture is  ready  for  use.  It  is  hauled  to  the  street  and  spread  with  iron 
rakes  to  such  depth  as  will  give  the  required  thickness  when  compacted 
(the  finished  thickness  varies  between  1^  and  2j  inches).  The  re- 
duction of  thickness  by  compression  is  generally  about  40  per  cent. 

The  mixture  is  sometimes  laid  in  two  layers.  The  first  is  called 
the  binder  or  cushion=coat ;  it  contains  from  2  to  5  per  cent  more  cement 
than  the  surface-coat;  its  thickness  is  usually  -|  inch.  The  object  of  the 
binder  course  is  to  unite  the  surface  mixture  with  the  foundation,  which 
it  does  through  the  larger  percentage  of  cement  that  it  contains,  which, 
if  put  in  the  surface  mixture,  would  render  it  too  soft. 

The  paving  composition  is  compressed  by  means  of  rollers  and 
tamping  irons,  the  latter  being  heated  in  a  fire  contained  in  an  iron 
basket  mounted  on  wheels.  These  irons  are  used  for  tamping  such 
portions  as  are  inaccessible  to  the  roller — namely,  gutters,  around  man- 
hole heads,  etc. 

Two  rollers  are  sometimes  employed;  one,  weighing  5  to  6  tons 
and  of  narrow  tread,  is  used  to  give  the  first  compression;  and  the 
other,  weighing  about  10  tons  and  of  broad  tread,  is  used  for  finishing. 
The  amount  of  rolling  varies;  the  average  is  about  1  hour  per  1,000 
square  yards  of  surface.  After  the  primary  compression,  natural 
hydraulic  or  any  impalpable  mineral  matter  is  sprinkled  over  the  sur- 
face, to  prevent  the  adhesion  of  the  material  to  the  roller  and  to  give 
the  surface  a  more  pleasing  appearance.  When  the  asphalt  is  laid 
up  to  the  curb,  the  surface  of  the  portion  forming  the  gutter  is  painted 
with  a  coat  of  hot  cement. 

Although  asphaltum  is  a  bad  conductor  of  heat,  and  the  cement 


378 


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11 


HIGHWAY  CONSTRUCTION  HI 


retains  its  plasticity  for  several  hours,  occasions  may  and  do  arise 
through  which  the  composition  before  it  is  spread  has  cooled;  its  con- 
dition when  this  happens  is  analogous  to  hydraulic  cement  which  has 
taken  a  "set,"  and  the  same  rules  which  apply  to  hydraulic  cement  in 
this  condition  should  be  respected  in  regard  to  asphaltic  cement. 

The  proportions  of  the  ingredients  in  the  paving  mixture  are  not 
constant,  but  vary  with  the  climate  of  the  place  where  the  pavement 
is  to  be  used,  the  character  of  the  sand,  and  the  amount  and  character 
of  the  traffic  that  will  use  the  pavement.  The  range  in  the  proportion 
is  as  follows: 

Formula  for  Asphaltic  Paving  Mixture 

Asphalt  cement 12  to  15  per  cent. 

Sand 70  to  83    " 

Stone-dust .5  to  15    " 

A  cubic  yard  of  the  prepared  material  weighs  about  4,500  pounds,  and 
will  lay  the  following  amount  of  wearing-surface: 

1\  inches  thick 12  square  yards. 

2         "          "     IS      " 

1J       "  " 27      " 

One  ton  of  refined  asphaltum  makes  about  2,300  pounds  of  asphalt 
cement,  equal  to  about  3.4  cubic  yards  of  surface  material. 

Foundation.  A  solid,  unyielding  foundation  is  indispensable 
with  all  asphaltic  pavements,  because  asphalt  of  itself  has  no  power  of 
offering  resistance  to  the  action  of  traffic,  consequently  it  is  nearh 
always  placed  upon  a  bed  of  hydraulic  cement  concrete.  The  concrete 
must  be  thoroughly  set  and  its  surface  dry  before  the  asphalt  is  laid 
upon  it;  if  not,  the  water  will  be  sucked  up  and  converted  into  steam, 
with  the  result  that  coherence  of  the  asphaltic  mixture  is  prevented, 
and,  although  its  surface  may  be  smooth,  the  mass  is  really  honey- 
combed, so  that  as  soon  as  the  pavement  is  subjected  to  the  action  of 
traffic,  the  voids  or  fissures  formed  by  the  steam  appear  on  the  surface, 
and  the  whole  pavement  is  quickly  broken  up. 

Advantages  of  Asphalt  Pavement.  These  may  be  summed  up 
as  follows: 

(1)  Ease  of  traction. 

(2)  It  is  comparatively  noiseless  under  traffic. 

(3)  It   is   impervious. 

(4)  It  is  easily  cleansed. 

(5)  It  produces  neither  mud  nor  dust. 

(6)  It  is  pleasing  to  the  eye. 


379 


112  HIGHWAY  CONSTRUCTION 

(7)  It  suits  all  classes  of  traffic. 

(8)  There  is  neither  vibration  nor  concussion  in  traveling  over  it. 

(9)  It  is  expeditiously  laid,  thereby  causing  little  inconvenience 
to  traffic. 

(10)  Openings  to  gain  access  to  underground  pipes  are  easily 
made. 

(11)  It  is  durable. 

(12)  It  is  easily  repaired. 

Defects  of  Asphalt  Pavement.    These  are  as  follows: 

(1)  It  is  slippery  under  certain  conditions  of  the  atmosphere. 
The  American  asphalts  are  much  less  so  than  the  European,  on  account 
of  their  granular  texture  derived  from  the  sand.     The  difference  is 
very  noticeable;  the  European  are  as  smooth  as  glass,  while  the  Ameri- 
can resemble  fine  sandpaper. 

(2)  It  will  not  stand  constant  moisture,  and  will  disintegrate  if 
excessively  sprinkled. 

(3)  Under  extreme  heat  it  is  liable  to  become  so  soft  that  it  will 
roll  01*  creep  under  traffic  and  present  a  wavy  surface;  and  under  ex- 
treme cold  there  is  danger  that  the  surface   will  crack  and   become 
friable. 

(4)  It  is  not  adapted  to  grades  steeper  than  2-V  per  cent,  although 
it  is  in  use  on  grades  up  to  7.30  per  cent. 

(5)  Repairs  must  be  quickly  made,  for  the  material  has  little 
coherence,  and  if,  from  irregular  settlement  of  foundation  or  local  vio- 
lence, a  break  occurs,  the  passing  wheels  rapidly  shear  off  the  sides  of 
the   hole,    and    it    soon    assumes    formidable    dimensions. 

The  strewing  of  sand  upon  asphalt  renders  it  less  slippery ;  but  in 
addition  to  the  interference  of  the  traffic  while  this  is  being  done,  there 
are  further  objections — namely,  the  possible  injury  by  the  sand  cutting 
into  the  asphalt,  the  expense  of  labor  and  materials,  and  the  mud 
formed,  which  has  afterwards  to  be  removed. 

Although  pure  asphaltum  is  absolutely  impervious  and  insoluble 
in  either  fresh  or  salt  wafer,  yet  asphalt  pavements  in  the  continued 
presence  of  water  are  quickly  disintegrated.  Ordinary  rain  or  daily 
sprinkling  does  not  injure  them  when  they  are  allowed  to  become  per- 
fectly dry  again.  The  damage  is  most  apparent  in  gutters  and  adja- 
cent to  overflowing  drinking  fountains.  This  defect  has  long  been 
recognized;  and  various  measures  have  been  taken  to  overcome  it,  or 


380 


HIGHWAY  CONSTRUCTION 


113 


at  least  to  reduce  it  to  a  minimum.  In  some  cities,  ordinances  have 
been  passed,  seeking  to  regulate  the  sprinkling  of  the  streets;  and  in 
many  places  the  gutters  are  laid  with  stone  or  vitrified  brick  (see  Figs. 


Fig.  64. 

64  and  65),  while  in  others  the  asphalt  is  laid  to  the  curb,  a  space  of 
12  to  15  inches  along  the  curb  being  covered  with  a  thin  coating  of 
asphalt  cement. 

Asphalt  laid  adjoining  center-bearing  street-car  rails  is  quickly 
broken  down  and  destroyed.  This  defect  is  not  peculiar  to  asphalt. 
All  other  materials  when  placed  in  similar  positions  are  quickly  worn. 
Granite  blocks  laid  along  such  tracks  have  been  cut  into  at  a  rate  of 
more  than  half  an  inch  a  year.  The  frequent  entering  and  turning  off 
of  vehicles  from  car  tracks  is  one  of  the  severest  tests  that  can  be 


Asphalt 


3 rich    Gutter 


Curb 


Fig.  65. 

applied  to  any  paving  material;  moreover,  the  gauge  of  trucks  and 
vehicles  is  frequently  greater  than  that  of  the  rails,  so  one  wheel  runs 
on  the  rail  and  the  other  outside.  The  number  of  wheels  thus  travel- 
ing in  one  line  must  quickly  wear  a  rut  in  any  material  adjoining  the 
center-bearing  rail. 

To  obviate  the  destruction  of  asphalt  in  such  situations,  it  is  usual 
to  lay  a  strip  of  granite  block  or  brick  paving  along  the  rail.  This 
pavement  should  be  of  sufficient  width  to  support  the  wheels  of  the 
widest  gauge  using  the  street. 


381 


114  HIGHWAY  CONSTRUCTION 

The  burning  of  leaves  or  making  of  fires  on  asphalt  pavements 
should  not  be  permitted,  as  it  injures  the  asphalt,  and  the  paving  com- 
panies cannot  be  compelled  to  repair  the  damaged  places  without 
compensation. 

Asphalt  Blocks.  Asphalt  paving  blocks  are  formed  from  a  mix- 
ture of  asphaltic  cement  and  crushed  stone  in  the  proportion  of  8  to  12 
per  cent  of  cement  to  88  and  92  per  cent  of  stone.  The  materials  are 
heated  to  a  temperature  of  about  300°  F.,  and  mixed  while  hot  in  a 
suitable  vessel.  When  the  mixing  is  complete,  the  material  is  placed 
in  moulds  and  subjected  to  heavy  pressure,  after  which  the  blocks  are 
cooled  suddenly  by  plunging  into  cold  water. 

The  usual  dimensions  of  the  blocks  are  4  inches  wide,  3  inches 
deep,  and  12  inches  long. 

Foundation.  The  blocks  are  usually  laid  upon  a  concrete  founda- 
tion with  a  cushion-coat  of  sand  about  |  inch  thick.  They  are  laid 
with  their  length  at  right  angles  to  the  axis  of  the  street,  and  the  longitu- 
dinal joints  should  be  broken  by  a  lap  of  at  least  4  inches.  The  blocks 
are  then  either  rammed  with  hand  rammers  01  rolled  with  a  light  steam 
roller,  the  surface  being  covered  with  clean,  fine  sand ;  no  joint  filling  is 
used,  as,  under  the  action  of  the  sun  and  traffic,  the  blocks  soon  become 
cemented. 

The  advantages  claimed  for  a  pavement  of  asphalt  blocks  over  a 
continuous  sheet  of  asphalt  are:  (1)  That  they  can  be  made  at  a 
factory  located  near  the  materials,  whence  they  can  be  transported  to 
the  place  where  they  are  to  be  used  and  can  be  laid  by  ordinary  paviors, 
whereas  sheet  pavements  require  special  machinery  and  skilled  labor; 

(2)  that  they  are  less  slippery,  owing  to  the  joints  and    the  rougher 
surface  due  to  the  use  of  crushed  stone. 

Asphalt  Macadam — Bituminous  Macadam.  Recently  it  has  been 
proposed  to  use  asphalt  as  a  binding  material  for  broken  stone. 
There  are  two  patented  processes — the  Whinery  and  the  Warren — 
which  differ  slightly  in  details. 

The  advantages  claimed  for  these  methods  are:  (1)  The  first 
coat  will  be  materially  less;  (2)  it  will  offer  a  better  foothold  for  horses; 

(3)  it  will  be  at  least  as  durable  as  the  ordinary  sheet  asphalt;  (4)  it  will 
not  shift  under  traffic  and  roll  into  waves;  (5)  it  will  not  crack;  (6)  it 


982 


HIGHWAY  CONSTRUCTION 


115 


can  be  repaired  more  cheaply  and  with  less  skilled  labor  than  can  the 
ordinary  sheet  asphalt. 

Tools  Employed  in   Construction   of  Asphalt  Pavements.    The 


Fig.  66.    Steam  Roller. 


Fig.  67.     Asphalt  Tools. 


tools  used  in  laying  sheet  asphalt  pavements  comprise  iron  rakes; 
hand  rammers;  smoothing  irons  (Fig.  67);  pouring  pots  (Fig.  69); 


116 


HIGHWAY  CONSTRUCTION 


hand  rollers,  either  with  or  without  a  fire-pot  (Fig.  68);  and  steam 
rollers,  with  or  without  provision  for  heating  the  front  roll  (Fig.  66). 
These  rollers  are  different  in  construction,  appearance,  and  weight 


Fig.  68.    Hand  Hollers. 


Fig.  69.    Pouring  Pots. 

from  those  employed  for  compacting  broken  stone.     The  difference 
is  due  to  the  different  character  of  the  work  required. 

The  principal  dimensions  of  a  five-ton  roller  are  as  follows : 

•Front  roll  or  steering-wheel 30  to  32  inches  diameter. 

Rear  roll  or  driving-wheel 48       " 

Width  of  front  roll 40       " 

"       "  rear      "     40       " 

Extreme  length    14  feet. 

"         height 7  to  8  feet. 

Water  capacity 80  to  100  gallons. 

Coal          "        200  pounds. 


384 


HIGHWAY  CONSTRUCTION  11? 


FOOTPATHS— CURBS— GUTTERS. 

A  footpath  or  walk  is  simply  a  road  under  another  name — a  road 
for  pedestrians  instead  of  one  for  horses  and  vehicles.  The  only 
difference  that  exists  is  in  the  degree  of  service  required ;  but  the  con- 
ditions of  consruction  that  render  a  road  well  adapted  to  its  object  are 
very  much  the  same  as  those  required  for  a  walk. 

The  effects  of  heavy  loads  such  as  use  carriageways  are  not  felt 
upon  footpaths;  but  the  destructive  action  of  water  and  frost  is  the 
same  in  either  case,  and  the  treatment  to  counteract  or  resist  these 
elements  as  far  as  practicable,  and  to  produce  permanency,  must  be 
the  controlling  idea  in  each  case,  and  should  be  carried  out  upon  a 
common  principle.  It  is  not  less  essential  that  a  walk  should  be  well 
adapted  to  its  object  than  that  a  road  should  be;  and  it  is  annoying  to 
find  it  impassable  or  insecure  and  in  want  of  repair  when  it  is  needed 
for  convenience  or  pleasure.  In  point  of  economy,  there  is  the  same 
advantage  in  constructing  a  footway  skilfully  and  durably  as  there  is 
in  the  case  of  a  road. 

Width.  The  width  of  footwalks  (exclusive  of  the  space  occupied 
by  projections  and  shade  trees)  should  be  ample  to  accomodate  com- 
fortably the  number  of  people  using  them.  In  streets  devoted  entirely 
to  commercial  purposes,  the  clear  width  should  be  at  least  one-third 
the  width  of  the  carriageway;  in  residential  and  suburban  streets,  a 
very  pleasing  result  can  be  obtained  by  making  the  walk  one-half  the 
width  of  the  roadway,  and  devoting  the  greater  part  to  grass  and  shade 
trees. 

Cross  Slope.  The  surface  of  footpaths  must  be  sloped  so  that 
the  surface  water  will  readily  flow  to  the  gutters.  This  slope  need  not 
be  very  great;  |  inch  per  foot  will  be  sufficient.  A  greater  slope  with  a 
thin  coating  of  ice  upon  it,  becomes  dangerous  to  pedestrians. 

Foundation.  As  in  the  case  of  roadways,  so  with  footpaths,  the 
foundation  is  of  primary  importance.  Whatever  material  may  be  used 
for  the  surface,  if  the  foundation  is  weak  and  yielding,  the  surface  will 
settle  irregularly  and  become  extremely  objectionable,  if  not  danger- 
ous, to  pedestrians. 

Surface.     The  requirements  of  a  good  covering  for  sidewalks  are : 

(1)  It  must  be  smooth  but  not  slippery.  ' 

(2)  It  must  absorb  the  minimum  amount  of  water,  so  that  it 
may  dry  rapidly  after  rain. 


118  HIGHWAY  CONSTRUCTION 

(3)  It  must  not  be  easily  abraded. 

(4)  It  must  be  of  uniform  quality  throughout,  so  that  it  may 
wear  evenly. 

(5)  It  must  neither  scale  nor  flake. 

(6)  Its  texture  must  be  such  that  dust  will  not  adhere  to  it. 

(7)  It  must  be  durable. 

Materials.  The  materials  used  for  footpaths  are  as  follows: 
Stone,  natural  and  artificial;  wood;  asphalt;  brick;  tar  concrete;  and 
gravel. 

Of  the  natural  stones,  sandstone  (Milestone)  and  granite  are  ex- 
tensively employed. 

The  bluestone,  when  well  laid,  forms  an  excellent  paving  material. 
It  is  of  compact  texture,  absorbs  water  to  a  very  limited  extent,  and 
hence  soon  dries  after  rain;  it  has  sufficient  hardness  to  resist  abrasion, 
and  wears  well  without  becoming  excessively  slippery. 

Granite,  although  exceedingly  durable,  wears  very  slippery,  and 
its  surface  has  to  be  frequently  roughened. 

Slabs,  of  whatever  stone,  must  be  of  equal  thickness  throughout 

their  entire  area;  the 
edges  must  be  dressed 
true  to  the  square  for  the 
whole  thickness  (edges 
must  not  be  left  feather- 
ed as  shown  in  Fig.  70);  and  the  slabs  must  be  solidly  bedded  on  the 
foundation  and  the  joints  filled  with  cement-mortar. 

Badly  set  or  faultily  dressed  flagstones  are  very  unpleasant  to 
walk  over,  especially  in  rainy  weather;  the  unevenness  causes  pedes- 
trians to  stumble,  and  rocking  stones  squirt  dirty  water  over  their 
clothes. 

Wood  has  been  largely  used  in  the  form  of  planks;  it  is  cheap  in 
first  cost,  but  proves  very  expensive  from  the  fact  that  it  lasts  but  a 
comparatively  short  time  and  requires  constant  repair  to  keep  it 
from  becoming  dangerous. 

Asphalt  forms  an  excellent  footway  pavement;  it  is  durable  and 
does  not  wear  slippery. 

Brick.  Brick  of  suitable  quality,  well  and  carefully  laid  on  a 
concrete  foundation,  makes  an  excellent  footway  pavement  for  resi- 


380 


HIGHWAY  CONSTRUCTION  119 

dential  and  suburban  streets  of  large  cities,  and  also  for  the  main 
streets  of  smaller  towns.  The  bricks  should  be  a  good  quality  of 
paving  brick  (ordinary  building  brick  are  unsuitable,  as  they  soon 
wear  out  and  are  easily  broken) .  The  bricks  should  be  laid  in  parallel 
rows  on  their  edges,  with  their  length  at  right  angles  to  the  axis  of  the 
path. 

Curbstones.  Curbstones  are  employed  for  the  outer  side  of  foot- 
ways, to  sustain  the  coverings  and  form  the  gutter.  Their  upper  edges 
are  set  flush  with  the  footwalk  pavement,  so  that  the  water'  can  flov, 
over  them  into  the  gutters. 

The  disturbing  forces  which  the  curb  has  to  resist,  are  :  (1)  The 
pressure  of  the  earth  behind  it,  which  is  frequently  augmented  by 
piles  of  merchandise,  building  materials,  etc.  This  pressure  tends  to 
overturn  it,  break  it  transversely,  or  move  it  bodily  on  its  base.  (2) 
The  pressure  due  to  the  expansion  of  freezing  earth  behind  and  be- 
neath it.  This  force  is  most  frequent  where  the  sidewalk  is  partly 
sodded  and  the  ground  is  accordingly  moist.  Successive  freezing  and 
thawing  of  the  earth  behind  the  curb  will  occasion  a  succession  of 
thrusts  forward,  which,  if  the  curb  be  of  faulty  design,  will  cause  it.  to 
incline  several  degrees  from  the  vertical.  (3)  The  concussions  and 
abrasions  caused  by  traffic  To  withstand  the  destructive  effect  of 
wheels,  curbs  are  faced  with  iron;  and  a  concrete  curb  with  a  rounded 
edge  of  steel  has  been  patented  and  used  to  some  extent.  Fires  built 
in  the  gutters  deface  and  seriously  injure  the  curb.  Posts  and  trees 
set  too  near  the  curb,  tend  to  break,  displace,  and  destroy  it. 

The  use  of  drain  tiles  under  the  curb  is  a  subject  of  much  differ- 
ence of  opinion  among  engineers.  Where  the  subsoil  contains  water 
naturally,  or  is  likely  to  receive  it  from  outside  the  curb-lines,  the  use 
of  drains  is  of  decided  benefit;  but  great  care  must  be  exercised  in 
jointing  the  drain-tiles,  lest  the  soil  shall  be  loosened  and  removed, 
causing  the  curb  to  drop  out  of  alignment. 

The  materials  employed  for  curbing  are  the  natural  stones,  as 
granite,  sandstone  (bluestone),  etc.,  artificial  stone,  fire-clay,  and  cast 
iron. 

The  dimensions  of  curbstones  vary  considerably  in  different 
localities  and  according  to  the  width  of  the  footpaths;  the  wider  the 
path,  the  wider  should  be  the  curb.  It  should,  however,  never  be  lass 
than  8  inches  deep,  nor  narrower  than  4  inches.  Depth  is  necessary 


387 


120 


HIGHWAY  CONSTRUCTION 


to  prevent  the  curb  turning  over  toward  the  gutter.  It  should  never 
be  in  smaller  lengths  than  3  feet.  The  top  surface  should  be  beveled 
off  to  conform  to  the  slope  of  the  footpath.  The  front  face  should  be 
hammer-dressed  for  a  depth  of  about  6  inches,  in  order  that  there  may 
be  a  smooth  surface  visible  against  the  gutter.  The  back  for  3  inches 


Slo. 


Fig.  71. 

from  the  top  should  also  be  dressed,  so  that  the  flagging  or  other  paving 
may  butt  fair  against  it.  The  end  joints  should  be  cut  truly  square, 
the  full  thickness  of  the  stone  at  the  top,  and  so  much  below  the  top  as 
will  be  exposed ,  the  remaining  portion  of  the  depth  and  bottom  should 
be  roughly  squared,  and  the  bottom  should  be  fairly  parallel  to  the 
top.  (See  Figs.  71  and  72). 

Artificial  Stone.     Artificial  stone  is  being  extensively  used  as  a 


footway  paving  material.  Its  manufacture  is  the  subject  of  several 
patents,  and  numerous  kinds  are  to  be  had  in  the  market.  When 
manufactured  of  first-class  materials  and  laid  in  a  substantial  manner, 
with  proper  provision  against  the  action  of  frost,  artificial  stone  forms 
a  durable,  agreeable,  and  inexpensive  pavement. 


888 


HIGHWAY  CONSTRUCTION 


Pig.  73.    Tamper. 


The  varieties  most  extensively  used  in  the  United  States*are 
known  by  the  names  of  granolithic,  monolithic,  fcrrolithic,  kosmocrete, 
metalithic,  etc. 

The  process  of  manufacture  is  practically  the  same  for  all  kinds, 
the  difference  being  in  the  materials  em- 
ployed. The  usual  ingredients  are  Port- 
land cement,  sand,  gravel,  and  crushed 
stone. 

Artificial    stone    for  footway    pave- 
ments  is   formed  in  two  ways — namely, 
in    blocks    manufactured    at    a    factory, 
brought  on   the  ground,  and  laid  in  the 
same  manner  as  natural  stone;  or  the  raw 
materials  are  brought  upon  the  work,  pre- 
pared, and  laid  in  place,  blocks  being  formed  by  the  use  of  board 
moulds. 

The  manner  of  laying  is  practically  the  same  for  all  kinds.  The 
area  to  be  paved  is  excavated  to  a  mini- 
mum depth  of  8  inches,  and  to  such  great- 
er depths  as  the  nature  of  the  ground  may 
require  to  secure  a  solid  foundation.  The 
surface  of  the  ground  so  exposed  is  well 
compacted  by  ramming;  and  a  layer  of 
gravel,  ashes,  clinker,  or  other  suitable  material  is  spread  and  consoli- 
dated ;  on  this  is  placed  the  concrete  wearing  surface,  usually  4  inches 
thick.  As  a  protection  against  the  lifting 
effects  of  frost,  the  concrete  is  laid  in 
squares,  rectangles,  or  other  forms  hav- 
ing areas  ranging  from  6  to  30  square 
feet,  strips  of  wood  being  employed  to 
form  moulds  in  which  the  concrete  is 

placed.  After  the  concrete  is  set,  these  strips  are  removed,  leaving 
joints  about  half  an  inch  wide  between  the  blocks.  Under  some 
patents  these  joints  are  filled  with  cement;  under  others,  with  tarred 
paper;  and  in  some  cases  they  are  left  open. 

Tools  Employed  in  Construction  of  Artificial  Stone  Pavements. 
Tampers  (Fig.  73).  Cast  iron,  with  hickory  handle;  range  from  6 
by  8  inches  to  8  by  10  inches. 


Fig.  74.    Quarter-Round. 


Fig.  75.    Jointer. 


122 


HIGHWAY  CONSTRUCTION 


Quarter-Round,  (Fig.  74). 
for  forming  corners  and  edges. 


Fig.  76.    Cutter. 


Made  of  any  desired  radius.     Used 

Jointer  (Fig.  75).  Used  for 
tiimming  and  finishing  the  joints. 

Cutter  (Fig.  76).  Used  for  cut- 
ting the  concrete  into  blocks. 

Gutter  Tool  (Fig.  77).  Used 
for  forming  and  finishing  gutters. 

Imprint  Rollers  (Figs.  78  and 
79).  Here  are  shown  two  designs 
of  rollers  for  imprinting  the  surface 
of  artificial  stone  pavements  with 
grooves,  etc. 

SELECTING  THE  PAVEMENT 

The  problem  of  selecting  the  best  pavement  for  any  particular 
case  is  a  local  one,  not  only  for  each  city,  but  also  for  each  of  the  various 
parts  into  which  the  city  is  imperceptibly  divided;  and  it  involves  so 
many  elements  that  the  nicest  balancing  of  the  relative  values  for  each 
kind  of  pavement  is  required,  to  arrive  at  a  correct  conclusion. 

In  some  localities,  the  proximity  of  one  or  more  paving  materials 
determines  the  character  of  the  pavement; 
while  in  other  cases  a  careful  investigation 
may  be  required  in  order  to  select  the 
most  suitable  material.  Local  conditions 
should  always  be  considered;  hence  it  is 
not  possible  to  lay  down  any  fixed  rule  as  to  what  material  makes  the 
best  pavement. 

The  qualities  essential  to  a  good  pavement  may  be  stated  as 
follows : 

(1)  It  should  be  impervious. 

(2)  It  should  afford  good  foothold  for  horses. 

(3)  It  should  be  hard  and  durable,  so  as  to  resist  wear  and  dis- 
integration. 

(4)  It  should  be  adapted  to  every  grade. 

(5)  It  should  suit  every  class  of  traffic. 

(6)  It  should  offer  the  minimum  resistance  to  traction. 

(7)  It  should  be  noiseless. 

(8)  It  should  yield  neither  dust  nor  mud. 


390 


HIGHWAY  CONSTRUCTION 


123 


(9)  It  should  be  easily  cleaned. 

(10)  It  should  be  cheap. 

Interests  Affected  in  Selection.  Of  the  above  requirements, 
numbers  2,  4,  5,  and  0  affect  the  traffic  and  determine  the  cost  of  haul- 
age by  the  limitations  of  loads,  speed, 
and  wear  and  tear  of  horses  and  ve- 
hicles. If  the  surface  is  rough  or  the 
foothold  bad,  the  weight  of  the  load 
a  horse  can  draw  is  decreased,  thus  ne- 
cessitating the  making  of  more  trips  or 
the  employment  of  more  horses  and 
vehicles  to  move  a  given  weight.  A 
defective  surface  necessitates  a  reduc- 
tion in  the  speed  of  movement  and 
consequent  loss  of  time;  it  increases  the 
wear  of  horses,  thus  decreasing  their 
Fig.  ?8.  imprint  Roller.  jjfe  service  and  lessening  the  value  of 

their  current  services;  it  also  increases 
the  cost  of  maintaining  vehicles  and 
harness. 

Numbers  7,  8,  and  9  affect  the 
occupiers  of  adjacent  premises,  who 
suffer  from  the  effect  of  dust  and 
noise;  they  also  affect  the  owners  of 
said  premises,  whose  income  from 
rents  is  diminished  where  these  disad- 
vantages exist.  Numbers  3  and  10  af- 
fect the  taxpayers  alone — first,  as  to 
the  length  of  time  during  which  the 
covering  remains  serviceable;  and  sec- 
ond, as  to  the  amount  of  the  annual 

repairs.  Number  1  affects  the  adjacent  occupiers  principally  on 
hygienic  grounds.  Numbers  7  and  8  affect  both  traffic  and  occupiers. 
Problem  Involved  in  Selection.  The  problem  involved  in  the 
selection  of  the  most  suitable  pavement  consists  of  the  following 
factors:  (1)  adaptability;  (2)  desirability;  (3)  serviceability;  (4)  dura- 
bility; (5)  cost. 

Adaptability.     The  best  pavement  for  any  given  roadway  will 


801 


124  HIGHWAY  CONSTRUCTION 

depend  altogether  on  local  circumstances.  Pavements  must  be  adapt- 
ed to  the  class  of  traffic  that  will  use  them.  The  pavement  suitable 
for  a  road  through  an  agricultural  district  will  not  be  suitable  for  the 
streets  of  a  manufacturing  center;  nor  will  the  covering  suitable  for 
heavy  traffic  be  suitable  for  a  pleasure  drive  or  for  a  residential  district. 

General  experience  indicates  the  relative  fitness  of  the  several 
materials  as  follows: 

For  country  roads,  suburban  streets,  and  pleasure  drives — broken 
stone.  For  streets  having  heavy  and  constant  traffic — rectangular 
blocks  of  stone,  laid  on  a  concrete  foundation,  with  the  joints  filled 
with  bituminous  or  Portland  cement  grout.  For  streets  devoted  to 
retail  trade,  and  where  comparative  noiselessness  is  essential — asphalt, 
wood,  or  brick. 

Desirability.  The  desirability  of  a  pavement  is  its  possession  of 
qualities  which  make  it  satisfactory  to  the  people  using  and  seeing  it. 
Between  two  pavements  alike  in  cost  and  durability,  people  will  have 
preferences  arising  from  the  condition  of  their  health,  presonal  pre- 
judices, and  various  other  intangible  influences,  causing  them  to  select 
one  rather  than  the  other  in  their  respective  streets.  Such  selections 
are  often  made  against  the  demonstrated  economies  of  the  case,  and 
usually  in  ignorance  of  them.  Whenever  one  kind  of  pavement  is 
more  economical  and  satisfactory  to  use  than  is  any  other,  there  should 
not  be  any  difference  of  opinion  about  securing  it,  either  as  a  new 
pavement  or  in  the  replacement  of  an  old  one. 

The  economic  desirability  of  pavements  is  governed  by  the  ease 
of  movement  over  them,  and  is  measured  by  the  number  of  horses  or 
pounds  of  tractive  force  required  to  move  a  given  weight — usually  one 
ton — over  them.  The  resistance  offered  to  traction  by  different  pave- 
ments is  shown  in  the  following  table: 

Resistance  to  Traction  on  Different  Pavements 

TRACTIVE  RESISTANCE 
KIND  OP  PAVEMENT 


Pounds  per  ton 

In  terms  of  the  loud 

Asphalt  (sheet).... 

30  to    70 

1     to     a 

Brick  

15    "    40 

6  T  to  ^  7 
1       ••       1 

Cobblestones  
Stone-block 

50    "  100 
30    "     80 

rsnr      BTF 
i    "    i 

Wood-block  rectangular 

30     "    50 

•«  r      ?w 
i   "    i 

Wood-block  round    

6  7          fW 
1      "       1 

TO        ?T 

392 


HIGHWAY  OBSTRUCTION  125 


Serviceability.  The  serviceability  of  a  pavement  is  its  quality  of 
fitness  for  use.  This  quality  is  measured  by  the  expense  caused  to  the 
traffic  using  it — namely,  the  wear  and  tear  of  horses  and  vehicles,  loss 
of  time,  etc.  No  statistics  are  available  from  which  to  deduce  the 
actual  cost  of  wear  and  tear. 

The  serviceability  of  any  pavement  depends  in  great  measure 
upon  the  amount  of  foothold  afforded  by  it  to  the  horses — provided, 
however,  that  its  surface  be  not  so  rough  as  to  absorb  too  large  a  per- 
centage of  the  tractive  energy  required  to  move  a  given  load  over  it. 
Cobblestones  afford  excellent  foothold,  and  for  this  reason  are  largely 
employed  by  horse-car  companies  for  paving  between  the  rails;  but 
the  resistance  of  their  surface  to  motion  requires  the  expenditure  ot 
about  40  pounds  of  tractive  energy  to  move  a  load  of  1  ton.  Asphalt 
affords  the  least  foothold;  but  the  tractive  force  required  to  overcome 
the  resistance  it  offers  to  motion  is  only  about  30  pounds  per  ton. 

Comparative  Safety.  The  comparison  of  pavements  in  respect  of 
safety,  is  the  average  distance  traveled  before  a  horse  falls.  The 
materials  affording  the  best  foothold  for  horses  are  as  follows,  stated 
in  the  order  of  their  merit : 

(1)  Earth,  dry  and  compact. 

(2)  Gravel. 

(3)  Broken  stone   (macadam). 

(4)  Wood. 

(5)  Sandstone  and   brick. 
(0)     Asphalt. 

(7)     Granite  blocks. 

Durability.  The  durability  of  pavement  is  that  quality  which 
determines  the  length  of  time  during  which  it  is  serviceable,  and  does 
not  relate  to  the  length  of  time  it  has  been  down.  The  only  measure 
of  durability  of  a  pavement  if  the  amount  of  traffic  tonnage  it  will  bear 
before  it  becomes  so  worn  that  the  cost  of  replacing  it  is  less  than  the 
expense  incurred  by  its  use. 

As  a  pavement  is  a  construction,  it  necessarily  follows  that  there 
is  a  vast  difference  between  the  durability  of  the  pavement  and  the 
durability  of  the  materials  of  which  it  is  made.  Iron  is  eminently 
durable;  but,  as  a  paving  material,  it  is  a  failure. 

Durability  and  Dirt.  The  durability  of  a  paving  material  will 
vary  considerably  with  the  condition  of  cleanliness  observed.  One 


126  HIGHWAY  CONSTRUCTION 


inch  of  overlying  dirt  will  most  effectually  protect  the  pavement  from 
abrasion,  and  indefinitely  prolong  its  life.  But  the  dirt  is  expensive, 
it  injures  apparel  and  merchandise,  and  is  the  cause  of  sickness  and 
discomfort.  In  the  comparison  of  different  pavements,  no  traffic 
should  be  credited  to  the  dirty  one. 

Life  of  Pavements.  The  life  or  durability  of  different  pavements 
under  like  conditions  of  traffic  and  maintenance,  may  be  taken  as 
follows : 

Life  Terms  of  Various  Pavements 


MATERIAL 

LIFE  TERM 

Granite  block  

12  to  30  years 

Sandstone  
Asphalt  
Wood                                                .   .. 

(>  '•   12 
10  '    H 
3   •      7 

Limestone  
Hrii-k                                                                                      

1    '      3 

5  '       ? 

Macadam  

5   '       ? 

Cost.  The  question  of  cost  is  the  one  which  usually  interests 
taxpayers,  and  is  probably  the  greatest  stumbling-block  in  the  attain- 
ment of  good  roadways.  The  first  cost  is  usually  charged  against  the 
property  abutting  on  the  highway  to  be  improved.  The  result  is  that 
the  average  property  owner  is  always  anxious  for  a  pavement  that  costs 
little,  because  he  must  pay  for  it,  not  caring  for  the  fact  that  cheap 
pavements  soon  wear  out  and  become  a  source  of  endless  annoyance 
and  expense.  Thus  false  ideas  of  economy  always  have  stood,  and 
undoubtedly  to  some  extent  always  will  stand,  in  the  way  of  realizing 
that  the  best  is  the  cheapest. 

The  pavement  which  has  cost  the  most  is  not  always  the  best;  nor 
is  that  which  cost  the  least  the  cheapest;  the  one  which  is  truly  the  cheap- 
est is  the  one  which  makes  the  most  profitable  returns  in  proportion  to  the 
amount  expended  upon  it.  No  doubt  there  is  a  limit  of  cost  to  go  be- 
yond which  would  produce  no  practical  benefit ;  but  it  will  always  be 
found  more  economical  to  spend  enough  to  secure  the  best  results,  and 
this  will  always  cost  less  in  the  long  run.  One  dollar  well  spent  is 
many  times  more  effective  than  one-half  the  amount  injudiciously 
expended  in  the  hopeless  effort  to  reach  sufficiently  good  results.  The 
cheaper  work  may  look  as  well  as  the  more  expensive  for  the 
time,  but  may  very  soon  have  to  be  done  over  again. 

Economical  Benefit.     The  economic  benefit  of  a  good  roadway  is 


394 


HIGHWAY  CONSTRUCTION  127 

comprised  in  its  cheaper  maintenance;  the  greater  facility  it  offers  for 
traveling,  thus  reducing  the  cost  of  transportation;  the  lower  cost  of 
repairs  to  vehicles,  and  less  wear  of  horses,  thus  increasing  their  term 
of  serviceability  and  enhancing  the  value  of  their  present  service;  the 
saving  of  time;  and  the  ease  and  comfort  afforded  to  those  using  the 
roadway. 

First  Cost.  The  cost  of  construction  is  largely  controlled  by  the 
locality  of  the  place,  its  proximity  to  the  particular  material  used,  and 
the  character  of  the  f6undation. 

The  Relative  Economies  of  Pavements — whether  of  the  same 
kind  in  different  condition,  or  of  different  kinds  in  like  good  condition 
— are  sufficiently  determined  by  summing  their  cost  under  the  following 
headings  of  account : 

(1)  Annual  interest  upon  first  cost. 

(2)  Annual  expense  for  maintenance. 

(3)  Annual  cost  for  cleaning  and  sprinkling. 

(4)  Annual  cost  for  service  and  use. 

(5)  Annual  cost  for  consequential  damages. 

Interest  on  First  Cost.  The  first  cost  of  a  pavement,  like  any 
other  permanent  investment,  is  measurable  for  purposes  of  comparison 
by  the  amount  of  annual  interest  on  the  sum  expended.  Thus,  assum- 
ing the  worth  of  money  to  be  4ff/<>,  a  pavement  costing  $4  per  square 
yard  entails  an  annual  interest  loss  or  tax  of  $0.16  per  square  yard. 

Cost  of  Maintenance.  Under  this  head  must  be  included  all  out- 
lays for  repairs  and  renewals  which  are  made  from  the  time  when  the 
pavement  is  new  and  at  its  best  to  a  time  subsequent,  when,  by  any 
treatment,  it  is  again  put  in  equally  good  condition.  The  gross  sum 
so  derived,  divided  by  the  number  of  years  which  elapse  between  the 
two  dates,  gives  an  average  annual  cost  for  maintenance. 

Maintenance  means  the  keeping  of  the  pavement  in  a  condition 
practically  as  good  as  when  first  laid.     The  cost  will  vary  considerably 
depending  not  only  upon  the  material  and  the  manner  in  which  it  is 
constructed,  but  upon  the  condition  of  cleanliness  observed,  and  the  " 
quantity  and  quality  of  the  traffic  using  the  pavement. 

The  prevailing  opinion  that  no  pavement  is  a  good  one  unless, 
when  once  laid,  it  will  take  care  of  itself,  is  erroneous;  there  is  no  such 
pavement  All  pavements  are  being  constantly  worn  by  traffic  and 
by  the  action  of  the  atmosphere;  and  if  any  defects  which  appear  are 


395 


128  HIGHWAY  CONSTRUCTION 

not  quickly  repaired,  the  pavements  soon  become  unsatisfactory  and 
are  destroyed.  To  keep  them  in  good  repair,  incessant  attention  is 
necessary,  and  is  consistent  with  economy.  Yet  claims  are  made  that 
particular  pavements  cost  little  or  nothing  for  repairs,  simply  because 
repairs  in  these  cases  are  not  made,  while  any  one  can  see  the  need  of 
them. 

Cost  of  Cleaning  and  Sprinkling.  Any  pavement,  to  be  con- 
sidered as  properly  cared  for,  must  be  kept  dustless  and  clean.  While 
circumstances  legitimately  determine  in  many  cases  that  streets  must 
be  cleaned  at  daily,  weekly,  or  semi-weekly  intervals,  the  only  admis- 
sible condition  for  the  purpose  of  analysis  of  street  expenses  must  be 
that  of  like  requirements  in  both  or  all  cases  subjected  to  comparison. 

The  cleaning  of  pavements,  as  regards  both  efficiency  and  cost, 
depends  (1)  upon  the  character  of  the  surface;  (2)  upon  the  nature  of 
the  materials  of  which  the  pavements  are  composed.  Block  pave- 
ments present  the  greatest  difficulty;  the  joints  can  never  be  perfectly 
cleaned.  The  order  of  merit  as  regards  facility  of  cleansing,  is:  (1) 
asphalt,  (2)  brick,  (3)  stone,  (4)  wood,  (5)  macadam. 

Cost  of  Service  and  Use.  The  annual  cost  for  service  is  made  up 
by  combining  several  items  of  cost  incidental  to  the  use  of  the  pave- 
ment for  traffic — for  instance,  the  limitation  of  the  speed  of  movement, 
as  in  cases  where  a  bad  pavement  causes  slow  driving  and  consequent 
loss  of  time;  or  cases  where  the  condition  of  a  pavement  limits  the 
weight  of  the  load  which  a  horse  can  haul,  and  so  compels  the  making 
of  more  trips  or  the  employment  of  more  horses  and  vehicles;  or  cases 
where  conditions  are  such  as  to  cause  greater  wear  and  tear  of  vehicles, 
of  equipage,  and  of  horses.  If  a  vehicle  is  run  1,500  miles  in  a  year, 
and  its  maintenance  costs  $30  a  year,  then  the  cost  of  its  maintenance 
per  mile  traveled  is  two  cents.  If  the  value  of  a  team's  time  is,  say, 
$1  for  the  legitimate  time  taken  in  going  one  mile  with  a  load,  and  in 
consequence  of  bad  roads  it  takes  double  that  time,  then  the  cost  to 
traffic  from  having  to  use  that  one  mile  of  bad  roadway  is  $1  for  each 
load.  The  same  reasoning  applies  to  circumstances  where  the  weight 
of  the  load  has  to  be  reduced  so  as  to  necessitate  the  making  of  more 
than  one  trip.  Again,  bad  pavements  lessen  not  only  the  life-service 
of  horses,  but  also  the  value  of  their  current  service. 

Cost  for  Consequential  Damages.  The  determination  of  conse- 
quential damages  arising  from  the  use  of  defective  or  unsuitable  pave- 


396 


HIGHWAY  CONSTRUCTION  129 

ments,  involves  the  consideration  of  a  wide  array  of  diverse  circum- 
stances. Rough-surfaced  pavements,  when  in  their  best  condition, 
afford  a  lodgment  for  organic  matter  composed  largely  of  the  urine 
and  excrement  of  the  animals  employed  upon  the  roadway.  In 
warm  and  damp  weather,  these  matters  undergo  putrefactive  fer- 
mentation, and  become  the  most  efficient  agency  for  generating  and 
disseminating  noxious  vapors  and  disease  germs,  now  recognized  as 
the  cause  of  a  large  part  of  the  ills  afflicting  mankind.  Pavements 
formed  of  porous  materials  are  objectionable  on  the  same,  if  not  even 
stronger,  grounds. 

Pavements  productive  of  dust  and  mud  are  objectionable,  and 
especially  so  on  streets  devoted  to  retail  trade.  If  this  particular 
disadvantage  be  appraised  at  so  small  a  sum  per  lineal  foot  of  frontage 
as  $1 .50  per  month,  or  six  cents  per  day,  it  exceeds  the  cost  of  the  best 
quality  of  pavement  free  from  these  disadvantages. 

Rough-surfaced  pavements  are  noisy  under  traffic  and  insufferable 
to  nervous  invalids,  and  much  nervous  sickness  is  attributable  to  them. 
To  all  persons  interested  in  nervous  invalids,  this  damage  from  noisy 
pavements  is  rated  as  being  far  greater  than  would  be  the  cost  of  sub- 
stituting the  best  quality  of  noiseless  pavement;  but  there  are,  under 
many  circumstances,  specific  financial  losses,  measurable  in  dollars 
and  cents,  dependent  upon  the  use  of  rough,  noisy  pavements.  They 
reduce  the  rental  value  of  buildings  and  offices  situated  upon  streets 
so  paved — offices  devoted  to  pursuits  wherein  exhausting  brain  work 
is  required.  In  such  locations,  quietness  is  almost  indispensable, 
and  no  question  about  the  cost  of  a  noiseless  pavement  weighs  against 
its  possession,  When  an  investigator  has  done  the  best  he  can  to 
determine  such  a  summary  of  costs  of  a  pavement,  he  may  divide  the 
amount  of  annual  tonnage  of  the  street  traffic  by  the  amount  of  annual 
costs,  and  know  what  number  of  tons  of  traffic  are  borne  for  each  cent 
of  the  average  annual  cost,  which  is  the  crucial  test  for  any  comparison, 
;is  follows: 

(1)  Annual  interest  upon  first  cost $ 

(2)  Average  annual  expense  for  maintenance  and  renewal . . . 

(3)  Annual  cost  for  custody  (sprinkling  and  cleaning) 

(4)  Annual  cost  for  service  and  use 

(.5)  Annual  cost  for  consequential  damages 

Amount  of  average  annual  cost 

Annual  tonnage  of  traffic 

Tons  of  traffic  for  each  cent  of  cost 

Gross  Cost  of  Pavements.     Since  the  cost  of  a  pavement  depends 


397 


130  HIGHWAY  CONSTRUCTION 


upon  the  material  of  which  it  is  formed,  the  width  of  the  roadway,  the 
extent  and  nature  of  the  traffic,  and  the  condition  of  repair  and  clean- 
liness in  which  it  is  maintained,  it  follows  that  in  no  two  streets  is  the 
endurance  or  the  cost  the  same,  and  the  difference  between  the  highest 
and  lowest  periods  of  endurance  and-  amount  of  cost  is  very  con- 
siderable. 

The  comparative  cost  of  the  various  street  pavements,  including 
interest  on  first  cost,  sinking  fund,  maintenance,  and  cleaning,  when 
reduced  to  a  uniform  standard  traffic  of  100,000  tons  per  annum  for 
each  yard  in  width  of  the  carriageway,  is  about  as  follows : 
Comparative  Cost  of  Various  Pavements 


MATERIAL 

ANNUAL  COST 
PEK  SQ.  YD. 

Granite  blocks  
Asphalt  street  
Brick... 
Wood  

$0.25 
0.40 
0.35 
0.60 

398 


REVIEW  QUESTIONS. 


PRACTICAL  TEST  QUESTIONS. 

In  the  foregoing  sections  of  this  Cyclopedia  nu- 
merous illustrative  examples  are  worked  out  in 
detail  in  order  to  show  the  application  of  the 
various  methods  and  principles.  Accompanying 
these  are  examples  for  practice  which  will  aid  the 
reader  in  fixing  the  principles  in  mind. 

In  the  following  pages  are  given  a  larg°.  num- 
ber of  test  questions  and  problems  which  afford  a 
valuable  means  of  testing  the  reader's  knowledge 
of  the  subjects  treated.  They  will  be  found  excel- 
lent practice  for  those  preparing  for  Civil  Service 
Examinations.  In  some  cases  numerical  answers 
are  given  as  a  further  aid  in  this  work. 


399 


REVIEW    QUESTIONS 

ON      THK      SUBJKOT      OK 

BRIDGE    ENGINEERING 


1.  Write  a  short  history  of  early  bridges. 

2.  Define:     Truss,   bridge   truss,   truss  bridge,  girders,  and 
girder  bridges. 

3.  Draw  an  outline  of  a  through  bridge,  and  also  an  outline  of 
a  deck  bridge. 

4.  Make  an  outline  diagram  of   n  truss,  and  write  the  names 
of  the  various  parts  on  the  respective  members. 

5.  Make   an   outline   diagram   of  a   Warren,   Howe,   Pratt, 
bowstring,  and  Baltimore  truss. 

6.  Compute  the  weight  of  steel  in  a  130-foot  highway  bridge 
whose  trusses  are  16  feet  center  to  center,  given  W  =  34  +  226  + 
0.1G6Z  +  0.71. 

7.  Compute  the  weight  of  steel  in  a  deck  plate-girder  span  of 
100  feet.     Loading,  E  50.     Given  W  =  124.0  +  12. 01. 

8.  WTiat  are  equivalent  uniform  loads? 

9.  WTiat  is  Cooper's  E  40  loading? 

10.  Prove  that  the  stress  in  a  diagonal  of  a  horizontal  chord 
truss  with  a  simple  web  system  is  V  sec  <£. 

1 1 .  Prove  that  the  chord  stress  is  M  -r-  h,  where  M  is  the  moment 
at  the  point,  and  h  is  the  height  of  the  truss. 

12.  Prove  that  the  load  must  be  on  the  segment  of  the  span  to 
the  right  of  the  section  to  produce  the  maximum  positive  shear. 

13.  Compute   the  maximum   positive  and  negative  live-load 
shears  in  a  13-panel  Howe  truss,  the  live  panel  load  being  40  000 
pounds. 


401 


REVIEW     QUESTIONS 


O  IV      THE      S   IT  B  J  K  <3  T      O  K 


BRIDGE    ENGINEERING 


'ART      II 


1.  Write  an  essay  of  200  words  on  the  economic  considerations 
governing  the  decision  to  build  and  the  decision  as  to  what  kind  of 
bridge  to  employ. 

2.  What  determines  the  height  and  width  of  railroad  truss 
bridges? 

'3.     Draw  a  clearance  diagram  for  a  bridge  on  a  straight  track, 
and  state  what  allowance  should  be  made  if  the  bridge  is  on  a  curve. 

4.  Describe  a  stress  sheet,  and  tell  what  should  be  on  it. 

5.  Make  a  sketch  of  a  cross-section  of  a  deck  plate-girder, 
showing  the  cross-ties,  guard-rails,  and  rails  in  place. 

G.     Make  a  sketch  showing  how  tracks  on  curves  are  con- 
structed. 

7.  What  is  the  span  under  coping,  the  span  center  to  center  of 
bearings,  and  the  span  over  all? 

8.  Design  a  tie  for  Cooper's  E  50  loading. 

9.  If  the  end  shear  of  a  plate-girder  is  394  500  pounds,  design 
the  web  section,  it  being  108  inches  deep. 

10.  If  the  dead-load  moment  is  8  489  000  pound-inches  and 
the  live-load  moment  is  30  010  000  pound-inches,  design  the  flange, 
if  the  distance  back  to  back  of  flange  angle,  is  7  feet  6i  inches,  it  being 
assumed  that  the  web  does  not  take  any  bending  moment. 

11.  If,  in  the  girder  of  Question  10,  above,  the  web  were  90  by 
^-irich*  design  the  flange,  considering  |  of  the  gross  area  of  the  web 
as  effective  flange  area. 


REVIEW    QUESTIONS 


<»*      THE      HUB  .1  K  C  T      <  >  IT 


11 1 G  11  WAY    CONSTRUC rr ION 


1 .  Fjxm  what  does  the  ease  with  which  a  vehicle  can  he  moved 
on  a  road  depend? 

2.  \\  hat  kind  of  a  road  surface  offers  the  greatest  resistance  to 
traction? 

3.  How  may  the  power  required  to  draw  a  vehicle  over  a  pro- 
jecting stone  be  calculated? 

4.  What  effect  has  gravity  on  the  load  a  horse  can  pull? 

5.  Under  what  condition  is  the  tractive  power  of  a  horse  de- 
creased? 

G.     What  are  the  best  methods  for  improving  sand  roads? 
7      State  briefly  how  earth  is  loosened  and  transported  and  the 
conditions  under  which  each  method  is  most  advantageous? 

8.  What  are  the  essential  requisites  for  securing  a  good  gravel 
road? 

9.  How  should  gravel  roads  be  repaired? 

10.  State  the  considerations  that  control  the  maximum  grade. 

11.  How  should  different  grades  be  joined? 

12.  What  considerations  control  the  width  of  a  road? 

13.  What  is  the  essential  quality  of    a  stone  used  for  road 
covering? 

14.  What  should  be  the  shape  and  size  of  broken  stone? 

15.  For  a  light  traffic  road  what  thickness  should  the  layer  of 
broken  stone  have? 

16.  How  should  the  foundation  for  the  broken  stone  be  pre- 
pared? 


403 


REVIEW    QUESTIONS 


ON      THE      SUBJECT     OF 


HIG-HWAY    CONSTRUCTION 


1,  How   should    the   natural   soil  be   prepared    to  receive  a 
pavement  ? 

2.  In  ramming  blocks  in  the  pavement,  what  point  requires 
to  be  watched  ? 

8.     How  is  a  sand  cushion  prepared  for  use  ? 

4.  What  influences  the  durability  of  a  granite? 

5.  How  are  rectangular  stones  laid  on  steep  grades  ? 

6.  How  is  the  surface  and  sub-surface  drainage  of  streets 
provided  for? 

7.  What  are  the  principal  objections  to  wood  pavements? 

8.  What  determines  the  best  width  for  a  street? 

9.  In  filling  the  joints  with  gravel  and  bituminous  cement, 
what  should  be  the  condition  of  the  material? 

10.  What  controls  the  maximum  grade  for  a  given  street? 

11.  AVhat  varieties  of  wood  give  the  most  satisfactory  results? 

12.  To  what  tests  are  stones  intended  for  paving  subjected? 

13.  Do  cobblestones  form  a  satisfactory  pavement? 

14.  What  properties  should  a  stone  possess  to  produce  a  sat- 
isfactory  paving  block? 

15.  How  are  expansion  joints  formed  in  a  pavement? 

16.  What  is  the  most  suitable  material  for  the  foundation  of 
a  pavement? 

17.  Under  what  class  of  traffic  may  wood  be  used? 

18.  Upon  what  does  the  durability  of  a  pavement  depend? 

19.  What  materials  are  employed  for  filling  the  joints  be- 
tween the  paving  blocks? 


404 


INDEX 


The  page  numbers  of  this  volume  ivill  be  found  at  the  bottom  of  the 
pages;  the  numbers  at  the  top  refer  only  to  the  section. 


Page 


Page 


A 

Bridge  Engineering 

Asphalt  pavement 

374 

weights 

18 

advantages  of 

379 

bridge  design 

141 

defects  of 

380 

clearance  diagram 

147 

foundation 

379 

economic  considerations 

141 

materials  for 

374 

economic  proportions 

143 

tools  used  in  construction  of 

383 

floor  system 

150 

Asphaltic  paving  mixture,  formula  for 

379 

practical  considerations 

155 

Axle  friction 

276 

specifications 

150 

B 

stress  sheet 

150 

Baltimore  truss 

74 

weights  and  loadings 

148 

Belgian  block  pavement 
Bituminous  limestone 

352 
374 

problems 
Bridge  trusses,  definition  of 

135-139 
13 

Bowstring  truss 

64 

Bridges,  loads  for 

22 

live  loads 

22 

Brick  pavements 

360 

wind  loads 

24 

absorption  test 
advantages  of 

361 
363 

Bridges,  weights  of 
formula1  for 

18 
19 

cross-breaking  test 
crushing  test 
defects  of 

362 
363 

highway  spans 
railroad  spans 
Broken-stone  roads 

22 
21 
332 

foundation  for 

363 

rattler  test 

360 

C 

Bridge  analysis 

11 

Catch-basins 

347 

early  bridges 

11 

City  streets 

341 

truss  bridge  development 

12 

arrangement  of 

341 

Bridge  engineering                                    11-264 

asphalt  pavement 

374 

bibliography 

264 

Belgian  block  pavement 

352 

bridge  analysis 

11 

brick  pavements 

360 

definitions 

13 

catch-basins 

347 

descriptions 

13 

cobblestone  pavement 

352 

girder  spans 

117 

curbstones 

387 

history 

11 

drainage 

346 

loads 

22 

footpath 

385 

st  resses 

26 

foundations 

348 

theory 

26 

grades 

342 

trusses                                             16, 

53 

granite  block  pavement 

352 

Note.  —  For  page  numbers  see  foot  of  pages. 

405 


II 

INDEX 

Page 

Page 

City  streets 

D 

gutters 

347       Deck  bridges,  definition  of 

14 

stone-block  pavements 

350       Drainage  of  roads 

298 

transverse  contour 

346       Drains,  fall  of 

301 

width  of 

341                                                E 

wood  pavements 

369 

Cobblestone  pavements 

352       Earth 

313 

Concrete 

349       Earth  roads 

316 

Concrete-mixing  machine 

368       Earthenware  pipe  culverts 

308 

Country  roads 

207       Earthwork 

310 

drainage 

•»()£                balancing  cuts  and  fills 

310 

culverts 

304                classification  of 

313 

fall  of  drains 

301                embankments  on  hillsides 

314 

side  ditches 

301               prosecution  of 

314 

of  surface 

302                shrinkage  of 

312 

water  breaks 

303               slopes 

311 

earthwork 

310       Embankments  on  hillsides 

314 

general  considerations 

Engine  loads  in  computing  stresses 

83 

axle  friction. 

276                maximum  moments,  position  of  wheel 

effect  of  springs  on  ve 

hides             277                                  loads  for 

91 

frict  ion 

267               maximum  shear,  position  of  wheel 

loss  of  tractive  power 

on  inclines    274                                  lo:lds  for 

89 

object  of  roads 

267                                                   F 

resistance  of  air 

Final  stresses 

1  10 

resistance  to  rolling 

Floor-l>eams,  moments  and  shears  in 

117 

tractive  power  and  gr 

Clients          272        FloQr  systems 

18 

location  of 

Footpaths 

385 

bridge  sites 

Forces,  resolution  of 

27 

cross  levels 

283 

examples 

284                                                     G 

final  selection 

283       Girder  bridges,  definition  of 

13 

intermediate  towns 

286       Girder  spans 

117 

levels 

moments  in  plate-girders 

119 

map 

moments  and  shears  in  floor-l>eam 

117 

memoir 

shears  in  plate-girders 

128 

profile 

283               stresses  in  plate-girders 

134 

reconuoissance 

278       Girders,  definition  of 

13 

topography 

28  !        Grades 

road  coverings 

OOQ               establishing 

294 

maximum 

291 

transverse  contour 

296 
minimum 

293 

width 

undulating 

293 

Creosoting 

371       Gradient 

291 

Culverts 

304       Grading  tools 

31!) 

jointing 

308                c:lrts 

323 

materials  for 

307                draining-tools 

32!) 

Curbstones 

387                dump  cars 

324 

Note.  —  For  page  numbers  see  fo 

ot  of  pages. 

406 


INDEX 


III 


Page 

Pago 

Grading  tools 

Mountain  roads 

287 

dump   wagons 

325 

alignment 

289 

horse  rollers 

329 

construction  profile 

290 

mechanical  graders 

325 

establishing  grade 

294 

picks 

319 

final  location 

290 

ploughs 

319 

gradient 

291 

road  machine 

327 

halting  places 

288 

scrapers 

321 

level  stretches 

294 

shovels 

319 

loss  of  height 

288 

sprinkling  carts 

330 

maximum  grade 

291 

surface  graders 

327 

minimum  grade 

293 

wheelbarrows 

322 

undulating  grades 

293 

Granite  block  pavement, 

352 

water  on 

28  K 

Gravel  heaters 

309 

/.ig/ags 

290 

Gravel  roads 

330 

P 

Glitters 

347 

Parabolic  truss 

H4 

11 

Pavements 

348 

Hard  pan 

313 

asphalt 

374 

Highway  bridges,  live  loads  for 

22 

Helgian  block 

352 

Highway  construction,                            2G7 

-398 

brick 

3«0 

city  streets 

341 

cobblestone 

352 

country  roads 

207 

concrete  foundation  for 

349 

drainage 

298 

cost 

394 

earthwork 

310 

granite  block 

352 

grading  tools 

319 

selecting 

390 

mountain  roads 

287 

stone  block 

350 

pavements 

348 

wood 

309 

road  coverings 

330 

Plate-girder  railway-span  design 

1  5fi 

Highway  spans,  actual  weights  of 

22 

bearings 

199 

Howe  truss 

59 

cross-frames 

181 

I 

determination  of  class 

166 

Inclines,  loss  of  tractive  power  on 

274 

determination  of  span 

157 

Iron  pii>e  culverts 

309 

flanges 

lt>3 

lateral  systems 

181 

K 

masonry  plan 

168 

Knee-braces,  definition  of 

15 

stiffeners 

192 

L 

stress  sheet 

202 

ties*  and  guard-rails 

159 

Lateral  bracing,  definition  of 

15 

web,  economic  depth  of 

1«2 

Live  load,  position  of,  for  maximum 

web  splice 

195 

positive  and  negative  shears    38 

Plate-girders 

LOOSJ  rock 

313 

moments  in 

1  19 

M 

shears  in 

128 

Maximum  and  minimum  stresses 

50 

stresses  in 

134 

Mechanical  graders 

325 

Pony-truss  bridge,  definition  of 

14 

Melting  furnaces 

369 

Portals,  definition  of 

15 

Moments  in  plate-girders 

119 

Pratt  truss 

48,  53,  93 

Note.  —  For  page  numbers  see  foot  of  pages 

407 


IV 


INDEX 


R 


Railroad  spans,  actual  weights  of 
Railway  bridges,  live  loads  for 
Road  coverings 

broken-stone 

gravel 

Road  machines 
Roads 

country 

drainage  of 

earth 

mountain 

sand 
Roadways  on  rock  slopes 


Sand  roads 

Shears,  maximum  live-loud 

Shears  in  plate-girders 

Shoes  and  roller  nests 

Side  slopes 

Slopes 

covering  of 

form  of 

inclination  of 
Snow-load  stresses 
Solid  rock 
Steam-rollers 
Stone  block  pavements 
Street  grades 


snow-load 

wind-load 
Stresses  in  bridge  trusses 

in  chord  members 

counters 

engine  loads 

live-load  moments 

live-load  shears 

maximum  and  minimum 

moments  method 

notation  used 

resolution  of  forces  method 

Warren  truss  under  dead  load 

Warren  truss  under  live  load 

in  web  members 
Stresses  in  plate-girders 
Note. — For  page  numbers  see  foot  of 


Page 


21 
23 

332 
330 
327 

267 
298 
316 
287 
318 
'316 


318 
38 
128 
254 
311 
311 
312 
311 
311 
103 
313 
338 
350 
342 

103 
104 
26 
33 
47 
83 
44 
38 
50 
30 
35 
27 
35 
45 
31 
134 


Surface  graders 

Sway  bracing,  definition  of 


Page 

327 

15 


Tables 

bridges,  formula  for  weights  of  19 

bridges,  types  of  for  various  spans  142 
dead-load  chord  stresses                     53.  61 

dead-load  stresses  in  diagonals  54 

deck  plate-girders,  weights  of  21 

floor-beam  reactions  119 
force  requked  to  draw  loaded  vehic!es 

over  inclined  roads  276 
force  of  wind  per  sq.  ft.  for  various 

velocities  277 

grade  data  292 
grades,  effects  of,  upon  load  horse  can 

draw  on  different  pavements  274 
gross  load  horse  can  draw  on  different 

kinds  of  road  surfaces  274 
impact  coefficient,  values  of  102 
impact  stresses  in  a  Pratt  truss  103 
lacing  bars,  thickness  of  229 
loads,  equivalent  uniform  24 
masonry  bearings,  length  of  158 
maximum  moments  in  a  deck  plate- 
girder  126 
maximum  moments,  determination  of 

position  of  wheel  loads  for  93 
maximum  shears  in  a  deck  plate- 
girder  133 
maximum  shear,  determination  of 

position  of  wheel  loads  for  90 
pavements,  comparative  cost  of 

various  398 

pavements,  life  term  of  various  394 

pins  for  country  highway  bridges  245 

pins  for  double-track  bridges  244 

pins  for  single-track  bridges  244 
plate-girder  bridges,,  width  of,  for 

various  spans  145 

reactions   for  a  deck  plate-girder  126 

reactions  for  a  through  plate-girder  123 
resistance  due  to  gravity  on  different 

inclinations  271 
resistance  to  traction  on  different 

pavements  392 


408 


INDEX 


Page 
Tables 

resistance   to    traction   on   different 

road  surfaces  268 

rise,  suitable  proportions  for  different 

paving  materials  297 

rivet  spacing  in  bottom  flange  177 

rivet  spacing  in  top  flange  179 

safe  spans  for  I-beams  151 

specific  gravity,  weight,  resistance  to 
crushing,   and  absorption 
power  of  stones  352 

standard  gauges  for  angles  1 75 

stresses  in  a  Pratt  truss  100 

tension  members  217 

tractive  power  of  horses  at  different 

velocities  273 

Trinidad    asphaltum,    average    com- 
position of  377 
trusses,  chronological  list  of  16 
wheel    position,    moments    in    deck 

plate-girder  125 

wheel  position,  moments  in  a  through 

plate-girder  1 22 

wheel  position,  shears  in  a  through 

plate-girder  1 29 

wind  stresses  in  Pratt  truss  1 1 3 

Through  bridges,  definition  of  14 

Through  Pratt  railway-span  design  203 

determination  of  span  204 

end-post  239 

floor-beams  207 

intermediate  posts  225 

lateral  systems  251 

masonry  plan  203 

pins  243 

portal  245 

shoes  and  roller  nests  254 

Note. — For  page  numbers  see  foot  o/  pages. 


Page 
Through  Pratt  railway-span  design 

stress  sheet  262 

stringers  205 

tension  members  215 

top  chord  231 

transverse  bracing  248 

Transverse  grade  345 

Trinidad  asphaltum  375 

Truss  bridge  development  1 2 

Truss,  members  of  14 

Truss  bridge,  definition  of  13 

Trusses,  classes  of  16 

chord  characteristics  16 

web  characteristics  18 

Trusses,  definition  of  13 

Trusses  under  dead  and  live  loads  53 

Baltimore  74 

bowstring  64 

Howe  59 

parabolic  64 

Pratt  53 

Trusses  under  engine  loads  93 

Pratt  93 

W 
Warren  truss 

under  dead  loads  35 

under  live  load  45 

Water  breaks  303 

WTeb  splice  195 

Wind-load  stresses  104 

bottom  lateral  bracing  107 

overturning  effect  of  wind  on  train       110 

overturning  effect  of  wind  on  truss      1 09 

portals  and  sway  bracing  112 

top  lateral  system  104 

WTind  loads  24 

Wood  pavemenos  369 


409 


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'•  V 


